**Problem 6: Oscillations**A mass \( m \) is attached to a spring with spring constant \( k \) on a frictionless table. We stretch and release it a distance \( x_0 \) away from the resting position.- **(a)** Sketch the position, velocity, and acceleration plots (time on \( x \)-axis). - **(b)** What is the period if: - (i) the mass is doubled, - (ii) the spring constant is quadrupled, - (iii) or we double \( x_0 \) but the mass and spring constant remain unchanged?- **(c)** On one plot, sketch the total energy, kinetic energy, and elastic energy with time on the \( x \)-axis.- **(d)** When the mass is at the position \(-x_0/3\), what is the velocity?- **(e)** At what distance will the speed of the mass be half of its maximum speed?

Answered: Image /qna-images/answer/24914e06-3025-47b1-a7ad-cba428d84ae3.jpg

A mass m is attached to a spring with spring constant k on a frictionless table. We stretch and release it a distance to away from the resting position. (a) Sketch the position, velocity, and acceleration plots (time on x-axis). (b) What is the period if: (i) the mass is doubled, (ii) or the spring constant is quadrupled, and (iii) or we double ro but the mass and spring constant remain unchanged? (c) On one plot, sketch the total energy, kinetic energy, and elastic energy with time on the xr-axis. (d) When the mass is at the position -ro/3, what is the velocity? (e) At what distance will the speed of the mass be half of its maximum speed?

A mass m is attached to a spring with spring constant k on a frictionless table. We stretch and release it a distance to away from the resting position. (a) Sketch the position, velocity, and acceleration plots (time on x-axis). (b) What is the period if: (i) the mass is doubled, (ii) or the spring constant is quadrupled, and (iii) or we double ro but the mass and spring constant remain unchanged? (c) On one plot, sketch the total energy, kinetic energy, and elastic energy with time on the xr-axis. (d) When the mass is at the position -ro/3, what is the velocity? (e) At what distance will the speed of the mass be half of its maximum speed?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

cle final answer lo Name towano ipali s 6. A mass on a spring vibrates horizontally on a smooth level surface. Its equation of motion is x(t) = 8 cost, where t is in second and x in centimeter. a. equilibrium position www. 0 heb erit bail ol Find the velocity (magnitude and direction) of the 2π/3. mass at time t = (Positive direction is to the right.) XELS XUS b. Describe in words what is going on to the mass. - What direction is it moving? - Is it speeding up or slowing down? 7. Find the derivative of the function. Simplify as much as possible. f(x) = sin(x) cos(1-x²) 2=175 f.(x f(x) fcall a S
Let there be a mass M = 0.5 kg on a spring. a) If we can hang the mass on the spring in a vertical position, how can we measure the spring constant, k, of the spring? Now we use this same spring in the horizontal configuration, assuming the mass slides on a frictionless horizontal surface. b) Assuming we have measured k to be 10 N/m, how many times will the system oscillate in a minute? (assume we displace the mass from equilibrium so that the system oscillates) c) If the mass passes through the equilibrium position with a velocity vo at time t = 0, what is the amplitude of the oscillation? d) Write the equation for the horizontal displacement of the block as a function of time.
A mass-spring system is set up so that the mass oscillates in the horizontal. The mass is 0.83_kg, and the spring has constant 44 N/m. The mass is pulled back so that the spring stretches 0.78_m, and then the mass is released. Find the speed of the mass when it is located at 0.39_m. (Assume there is no friction between the mass and the tabletop.) O 4.559_m/s O 4.918_m/s 4.181_m/s O 4.722_m/s 4.026_m/s 4.382_m/s
A certain spring has a scale to measure a maximum of 50 kg mass that can be stretched up to 20 cm. A body suspended from this balance, when displaced and released oscillates with a period of 0.6 s. Write the equation of oscillation and find the weight of the body.
The relation between gravitational acceleration and period for a 1.0-m long 1 pendulum is , where 7 is the period in seconds and & represents the 2 ng %3D gravitational acceleration in metres per second squared (m/s2). a) The gravitational acceleration at the surface of Earth is about 9.8 m/s2. Find the period of a pendulum 1.0 m long. b) The gravitational acceleration on the moon is approximately of the gravitational 1 acceleration at the surface of Earth. Determine the period of a pendulum 1.0 m long on the moon. c) Captain Mirk and Mr. Spark land on one of seven planets in the Alpha Beta system. Mr. Spark sets up a pendulum 1.0 m long, and Captain Mirk measures its period to be 1.304 s. Use the table to help you determine which planet they are on. Planet Ulu 3.6 Proserpine Wunderland Rutabaga Ada Sirius-Lee Ikona 6.8 13.5 19.7 23.2 31.1 54.0
Can you solve it plz
Hrlp
A spring with a mass of 2 kg has natural length 0.5 m. A force of 25.6 N isrequired to maintain it stretched to a length of 0.7 m. If the spring is stretched to a lengthof 0.7 m and then released with initial velocity O, find the position of the mass at anytime t.
A horizontal spring-mass system oscillates on a frictionless table. If the ratio of the mass to the spring constant is 0.028 kg·m/N, and the maximum speed of the mass was measured to be 4.2 m/s, the maximum extension of the spring will be_
The torce reguired to compress a non-standard spring as a qunction as. 04 displacement isgiven by the equation F(X) = -Asin (bx)t Kx, where A= 1L0N, b= 1l rad|m, and k- 58 NIm.0 IE M Part A:Enter a general equation in terms 07 the given I iiar 1iaNariables 7or the work requircol to comeress this spring7om positionx, txa: part Bi calculate the work done injouicr as the spring Is come ressed prmi itt bot Woe1=? Arom x=0t X,=38 cm. joulEJ asthe Spring Is Partc: calculate the Workdone in compressed 7rom x1=38cm To xg=69 cm
MärkxsfH) Problem 1: A mass of 20 grams stretches a spring by 10/169 meters. (a) Find the spring constant k, the angular frequency w, as well as the period T and frequency f of free undamped motion for this spring-mass system. (b) Find the general solution x(t) of the DE for the free spring-mass system. (c) Suppose that an exterior force of F(t) = 2.5 sin(12t) in Newtons acts on the spring-mass system. Find the equation of motion (the solution x(t)) of the system if the mass initially is at rest in its equilibrium position.