a pivot on a horizontal pole. The pendulum is set into motion such that its angular velocity w(t) as a function of time t is given by w(t) = (0.24 rad/s) sin(Ct +1 rad) where C is a constant with units of Hz. (a) Determine the value of the constant C and the initial angular velocity. Write an equation for the angle of the pendulum 0(t) as a function of time t. 6.831 Hz, 0.2020 rad/s, -(0.03513 rad) cos ((6.831 Hz) t + 1 rad)

a pivot on a horizontal pole. The pendulum is set into motion such that its angular velocity w(t) as a function of time t is given by w(t) = (0.24 rad/s) sin(Ct +1 rad) where C is a constant with units of Hz. (a) Determine the value of the constant C and the initial angular velocity. Write an equation for the angle of the pendulum 0(t) as a function of time t. 6.831 Hz, 0.2020 rad/s, -(0.03513 rad) cos ((6.831 Hz) t + 1 rad)

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter16: Oscillations

Section: Chapter Questions

Problem 8PQ: The expression x = 8.50 cos (2.40 t + /2) describes the position of an object as a function of time,...

See similar textbooks

Related questions

Q: A mass of 2 kg is suspended from a spring with a known constant of 10 Newton per centimetre and…

Q: A simple pendulum is made of a 50 cm-string and a bob of mass m. At t = 0, the pendulum is at its…

Q: In an oscillatory motion of a simple pendulum, the ratio of the maximum angular acceleration, e"max,…

Q: A large block P executes horizontal simple harmonic motion as it slides across a frictionless…

A: the maximum acceleration of simple harmonic motion will be, The angular frequency is,

Q: Chapter 15, Problem 049 The angle (with respect to the vertical) of a simple pendulum is given by e…

A: Write the given equation and substitute 0 s for t and 0.035 rad for θ.

Q: We often make the small angle approximation when analyzing pendulums. If we consider a pendulum that…

A: When the pendulum is analysed for periodic motions to evaluate value of g, then it is assumed that…

Q: In an oscillatory motion of a simple pendulum, the ratio of the maximum angular acceleration, e"max,…

A: Given: The ratio of the maximum angular acceleration (θ''max) to the maximum angular velocity…

Q: kg frictionless block is attached to an ideal spring with force constant 315 N/m. Initially the…

A: We know that the inSHM equation of motion is given as x(t) = A sinωt where A is amplitude ω is…

Q: A simple harmonic oscillator consists of a block of mass 2.50 kg attached to a spring of spring…

A: From the equation of angular velocity :ω=kmOn substituting the given values :ω=120 N/m2.50…

Q: For a simple pendulum, why must the pendulum's oscillations be small in order for the pendulum's…

A: For a simple pendulum , the oscillations is kept small so as to reduce the air resistance andmatch…

Q: A simple harmonic oscillator consists of a block of mass 1.40 kg attached to a spring of spring…

Q: A physics student uses a rod of an unknown length to demonstrate a physical pendulum. The period of…

A: Given: Physical Pendulum, Period of oscillation, T = 2.20 sMoment of Inertia, I = 0.15 ML2 Diagram:…

Q: In an engine, a piston oscillates with simple harmonic motion so that its position varies ac-…

A: Given data: - The expression for the position of the piston is x=5.00cos2t+π6. The time is t = 0.

Q: At what positions is the speed of a simple harmonic oscillator half its maximum? That is, what…

A: The equation to find the speed of the simple harmonic oscillator is v=vmax1-xA2 When the speed is…

Q: Your answer is partially correct. The pendulum in the figure consists of a uniform disk with radius…

Q: In an oscillatory motion of a simple pendulum, the ratio of the maximum angular acceleration, e"max,…

Q: For a damped oscillator with a mass of 330 g, a spring constant 100 N/m and a damping coefficient of…

A: Given data: Mass (m) = 330 g = 0.330 kg Spring constant (k) = 100 N/m Damping constant (b) = 56 g/s…

Q: A simple harmonic oscillator consists of a block of mass 2.10 kg attached to a spring of spring…

Q: A particle moving along the x axis in simple harmonic motion starts from its equilibrium position,…

A: Simple harmonic motion It is the to and from motion about equilibrium point.

Q: Calculate the period of oscillation of a 103 pendulum on a planet of density pp = 3.9 x 10° km, kg…

Q: Q.2: Consider a thin uniform rod of length a swinging as a physical pendulum about one end, where k…

Q: In an oscillatory motion of a simple pendulum, the ratio of the maximum angular acceleration, e"max,…

A: Here given the ratio of the maximum angular acceleration and maximum angular velocity of a simple…

Q: If period (T) can be expressed as T=aL^b, (L being length of pendulum), in a non linear form, the…

A: Given that:- T=aL^b (non linear form) And T=2π(L/g)^1/2 (Linear form)

Q: The moment of inertia of a physical pendulum of 3 kg oscillating at small angles around an axis at a…

A: (a) Here we know the time period of a physical pendulum for small angles is given by- T=2πImghand…

Q: If the object-spring system is described by x = (0.350 m) cos (1.25t), find the following. (a) the…

Q: A physical pendulum consisting of a uniform solid disk of mass 563 g and radius 14.4 cm supported in…

A: time period of simple harmonic motion =?

Q: Two blocks of masses m1=1.0 kg and m2=3 kg are connected by an ideal spring of force constant k=4…

A: The reduced mass of the system is μ=m1m2m1+m2

Q: The period of oscillation of a spring-and-mass system is 0.600 s and the amplitude is 4.97 cm. What…

A: Attending the second question, Combining Newton's second law and Hook's law, the acceleration of…

Q: A.3.3 Given the function governing the motion of a simple pendulum with mass 0.5 kg is 0 = 0.5…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: ) Suppose a pendulum with length L (meters) has angle e (radians) from the vertical. It can be shown…

Q: A block of mass 2.65 kg is to undergo simple harmonic oscillation along the x-axis at a frequency of…

A: Given:- A block of mass m= 2.65 kg is to undergo simple harmonic oscillation along the x-axis at a…

Q: A simple harmonic oscillator with a period of 1.43 sec and a mass of 4.20 kg has an initial velocity…

Q: A particle moving along the x axis in simple harmonic motion starts from its equilibrium position,…

Q: In the figure, a solid cylinder attached to a horizontal spring (k = 4.60 N/m) rolls without…

Q: In an oscillatory motion of a simple pendulum, the ratio of the maximum angular acceleration, e"max,…

Q: An oscillator consists of a block of mass 0.736 kg connected to a spring. When set into oscillation…

Q: An an oscillatory motion of a simple pendulum, the ratio of the maximum angular acceleration, 0"max,…

Q: A.3.3 Given the function governing the motion of a simple pendulum with mass 0.5 kg is 0 = 0.5…

Q: If the object-spring system is described by x = (0.340 m) cos (1.70t), find the following. (a) the…

A: (A) Consider the expression of the system: The general equation which resembles the equation of…

Q: In the figure, a solid cylinder attached to a horizontal spring (k = 4.60 N/m) rolls without…

Q: A simple pendulum is made of a 2 m-string and a bob of mass m. At t = 0, the pendulum is at its…

A: V =0.2 m/s Length A = 2m

Q: A mass of 0.38 kg is attached to a spring and set into oscillation on a horizontal frictionless…

A: A mass of 0.38 kg is attached to a spring and set into oscillation on a horizontal frictionless…

Q: At what positions is the speed of a simple harmonic oscillator half its maximum? That is, what…

Q: To double the total energy of a mass oscillating at the end of a spring, we need to Select one: O a.…

Q: An object oscillates with angular frequency ω = 8.0 rad/s. At t = 0, the object is at x = 4.0 cm…

A: Given, The angular frequency of the oscillations, ω=8 rad/s The position of the object at t=0, x0=4…

Q: The period of a torsion pendulum, for small angular displacements, is given by: T=2π√1/K where I is…

A: There are many types of errors. Some are random errors. Some are systematic error. Some are…

Question

Please show detailed steps its for a study guild I need to understand how to do the problem. Thank you! :)

a pivot on a horizontal pole. The pendulum is set into motion such that its angular
velocity w(t) as a function of time t is given by
w(t) = (0.24 rad/s) sin(Ct +1 rad)
where C is a constant with units of Hz.
(a) Determine the value of the constant C and the initial angular velocity. Write an
equation for the angle of the pendulum 0(t) as a function of time t. 6.831 Hz,
0.2020 rad/s, -(0.03513 rad) cos ((6.831 Hz) t + 1 rad)

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step 7

Step 8

Trending now

This is a popular solution!

Step by step

Solved in 8 steps with 9 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

The angular position of a pendulum is represented by the equation = 0.032 0 cos t, where is in radians and = 4.43 rad/s. Determine the period and length of the pendulum.
The expression x = 8.50 cos (2.40 t + /2) describes the position of an object as a function of time, with x in centimeters and t in seconds. What are the a. frequency, b. period, c. amplitude, and d. initial phase of the objects motion? e. What is the position of the particle at t = 1.45 s?
Suppose a pendulum with length L (meters) has angle θ (radians) from the vertical. It can be shown that θ as a function of time satisfies the differential equation:d2θdt2+gLsinθ=0where g=9.8 m/sec/sec is the acceleration due to gravity. For small values of θ we can use the approximation sin(θ)∼θ, and with that substitution, the differential equation becomes linear. A. Determine the equation of motion of a pendulum with length 1 meters and initial angle 0.1 radians and initial angular velocity dθ/dt 0.1 radians/sec. B. At what time does the pendulum first reach its maximum angle from vertical? (You may want to use an inverse trig function in your answer)seconds C. What is the maximum angle (in radians) from vertical? D. How long after reaching its maximum angle until the pendulum reaches maximum deflection in the other direction? (Hint: where is the next critical point?)seconds E. What is the period of the pendulum, that is the time for one swing back and forth?seconds
The frequency of oscillations of a simple pendulum is given by: j = Vi where g = 9.8 ms? and L is the length of the pendulum. At the time t = 0 two simple pendulums with lengths L1 and L2 had the same angle relative to the vertical direction. Determine the time at which they will have the same angle relative to the vertical direction again, given that L2/L, = 9/25 and f1 = 0.2 sª.
A body of mass m is suspended by a rod of length L that pivots without friction (as shown). The mass is slowly lifted along a circular arc to a height h. a. Assuming the only force acting on the mass is the gravitational force, show that the component of this force acting along the arc of motion is F = mg sin u. b. Noting that an element of length along the path of the pendulum is ds = L du, evaluate an integral in u to show that the work done in lifting the mass to a height h is mgh.
use the model for the period of a pendulum, T, such that T=2pi square root of L/g, where the length ofpendulum is L and the acceleration due to gravity is g. if the acceleration due to gravity is 9.8m/s^2 and the period equals 3s, find the length to the nearest cm. (100 cm= 1m)
Consider the nonlinear pendulum equation 0" + ) sin 0 = 0. The g denotes the gravitational acceleration and L denotes length. Suppose gravity g is 9.8 meters per second squared, and the length of the pendulum is 10 meters. Suppose the initial angle is 1 radians and initial angular velocity is 2.2 radians per second. Find the formula for the trajectory of the pendulum. Write theta" for 0. w? = help (formulas) Now find the maximum arly- : velocity of the pendulum given these initial conditions. Wmax help (numbers) Does the pendulum swing back and forth or keep rotating around its axis? ? The pendulum is swinging back and forth. N The pendulum is rotating around its axis.
O 0.15 sec In an oscillatory motion of a simple pendulum, the ratio of the maximum angular acceleration, O"max, to the maximum angular velocity, O'max, is Tt s^(-1). What is the time needed for the pendulum to complete two oscillations? O 1 sec O 2 sec O 4 sec O 0.5 sec O 0.25 sec
A pendulum in (Figure 1) has a swinging motion such that 0 = [-0.101 sin(4.55t) +0.3 cos (4.55t)] rad, where t is in seconds, and the arguments for the sine and cosine are in radians. Assume L = 0.4 m. Figure L 0 < 1 of 1 Part A Determine the magnitude of the velocity of the bob when 0 = 0º. Express your answer to three significant figures and include the appropriate units. v= Part B li Submit a = Value Submit μА Request Answer Determine the magnitude of the acceleration of the bob when 0 = 0°. Express your answer to three significant figures and include the appropriate units. Provide Feedback μA Value Units Request Answer ? Units ?
A mass of 1.23 kg is attached to an ideal spring with a spring constant of 235 N/m and set into oscillations with an amplitude of 0.08 m. What distance from equilibrium is the mass when its speed is 0.387 m/s? Just enter a number rounded to 3 significant figures. Assume proper SI Units.
A pendulum in (Figure 1) has a swinging motion such that 0 = [−0.101 sin(4.95t) + 0.3 cos(4.95t)] rad, where t is in seconds, and the arguments for the sine and cosine are in radians. Assume L = 0.2 m. Figure L 0 1 of 1 Part Determine the magnitude of the velocity of the bob when 0 = 0°. Express your answer to three significant figures and include the appropriate units. v = 0.313 Submit Part B ✓ Correct m a = Determine the magnitude of the acceleration of the bob when 0 = 0°. Express your answer to three significant figures and include the appropriate units. Previous Answers 1.46 Provide Feedback m Submit Previous Answers Request Answer ? X Incorrect; Try Again; 4 attempts remaining
In an oscillatory motion of a simple pendulum, the ratio of the maximum angular acceleration, O"max, to the maximum angular velocity, O'max, is TT s^(-1). What is the time needed for the pendulum to complete two oscillations?