Chapter 15, Problem 3Q

An automobile with a mass of 1000 kg, including passengers, settles 1.0 cm closer to the road for every additional 100 kg of passengers. It is driven with a constant horizontal component of speed 20 km/h over a washboard road with sinusoidal bumps. The amplitude and wavelength of the sine curve are 5.0 cm and 20 cm, respectively. The distance between the front and back wheels is 2.4 m. Find the amplitude of oscillation of the automobile, assuming it moves vertically as an undamped driven harmonic oscillator. Neglect the mass of the wheels and springs and assume that the wheels are always in contact with the road.

A mass is placed on a frictionless, horizontal table. A spring (k=100N/m) , which can be stretched or compressed, is placed on the table. A 5.00-kg mass is attached to one end of the spring, the other end is anchored to the wall. The equilibrium position is marked at zero. A student moves the mass out to x=4.0 cm and releases it from rest. The mass oscillates in SHM. (a) Determine the equations of motion. (b) Find the position, velocity, and acceleration of the mass at time t=3.00 s.

Which of the following statements is not true regarding a massspring system that moves with simple harmonic motion in the absence of friction? (a) The total energy of the system remains constant. (b) The energy of the system is continually transformed between kinetic and potential energy. (c) The total energy of the system is proportional to the square of the amplitude. (d) The potential energy stored in the system is greatest when the mass passes through the equilibrium position. (e) The velocity of the oscillating mass has its maximum value when the mass passes through the equilibrium position.

*11. ssm A spring is hanging down from the ceiling, and an object of mass m is attached to the free end. The object is pulled down, thereby stretching the spring, and then released. The object oscillates up and down, and the time T required for one complete up-and-down oscillation is given by the equation T = 27 Vmlk, where k is known as the spring constant. What must be the dimension of k for this equation to be dimensionally correct?

Chapter 15, Problem 049 GO The angle (with respect to the vertical) of a simple pendulum is given by e = 0mcos[(4.40 rad/s)t + p]. If at t = 0, 0 = 0.0200 rad and de/dt = -0.160 rad/s, what are (a) the phase constant p and (b) the maximum angle 0m? (Hint: Don't confuse the rate de/dt at which e changes with the w of the SHM.) Pivor point L. Is= Le F,cose Fgsine- (a) (6) (a) Number Unit (b) Number the tolerance is +/-2% Unit Click if you would like to Show Work for this question: Open Show Work

A massless spring hangs from the ceiling with a small object attached to its lower end. The object is initially held at rest in a position Y; such that the spring is at its rest length. The object is then released from y; and oscillates up and down, with its lowest position being 22 cm below yj. (a) What is the frequency of the oscillation? (b) What is the speed of the object when it is 8.5 cm below the initial position? (c) An object of mass 230 g is attached to the first object, after which the system oscillates with half the original frequency. What is the mass of the first object? (d) How far below y; is the new equilibrium (rest) position with both objects attached to the sping? (a) Number Units (b) Number Units |(c) Number Units (d) Number Units

In an oscillatory motion of a simple pendulum, the ratio of the maximum angular acceleration, e"max, to the maximum angular velocity, O'max, is rt s (-1). What is the time needed for the pendulum to complete one-half oscillation? 0.25 sec 0.5 sec 1 sec 2 sec O 4 sec The equation of motion of a particle in simple harmonic motion is given by: x(t) =

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 position of a 0.5 kg object attached to a spring in meters is given by: x(t) = 5 cos(2t + 0.5π). (a) Plot x(t) as a function of t, for 0 ≤ t ≤ 3π.(b) What is x(t) when t = 1.5 s and t = 7 s.(c) What is the: amplitude, period, frequency, and the spring constant?