17. Periodic Motion

A mass is oscillating with amplitude A at the end of a spring. How far (in terms of A) is this mass from the equilibrium position of the spring when the elastic potential energy equals the kinetic energy?

For the oscillating object in Fig. E14.4, what is its maximum acceleration?

For the oscillating object in Fig. E14.4, what is its maximum speed?

A 0.500-kg glider, attached to the end of an ideal spring with force constant k = 450 N/m, undergoes SHM with an amplitude of 0.040 m. Compute the total mechanical energy of the glider at any point in its motion

A 0.500-kg glider, attached to the end of an ideal spring with force constant k = 450 N/m, undergoes SHM with an amplitude of 0.040 m. Compute the speed of the glider when it is at x = -0.015 m.

A small block is attached to an ideal spring and is moving in SHM on a horizontal frictionless surface. The amplitude of the motion is 0.165 m. The maximum speed of the block is 3.90 m/s. What is the maximum magnitude of the acceleration of the block?

A small block is attached to an ideal spring and is moving in SHM on a horizontal, frictionless surface. The amplitude of the motion is 0.250 m and the period is 3.20 s. What are the speed and acceleration of the block when x = 0.160 m?

A pinball machine uses a spring launcher that is compressed 6.0 cm to launch a ball up a 22° ramp. Assume that the pinball is a solid uniform sphere of radius r = 1.0 cm and mass m = 25g. If it is rolling without slipping (Section 10–9) at a speed of 3.0 m/s when it leaves the launcher, what is the spring constant of the spring launcher?

A 500 g air-track glider attached to a spring with spring constant 10 N/m is sitting at rest on a frictionless air track. A 250 g glider is pushed toward it from the far end of the track at a speed of 120 cm/s. It collides with and sticks to the 500 g glider. What are the amplitude and period of the subsequent oscillations?

When the displacement of a mass on a spring is (½)A, what fraction of the energy is kinetic energy and what fraction is potential energy?

Two 500 g air-track gliders are each connected by identical springs with spring constant 25 N/m to the ends of the air track. The gliders are connected to each other by a spring with spring constant 2.0 N/m. One glider is pulled 8.0 cm to the side and released while the other is at rest at its equilibrium position. How long will it take until the glider that was initially at rest has all the motion while the first glider is at rest?

(I) A 1.28-kg mass oscillates according to the equation 𝓍 = 0.650 cos7.40 t where 𝓍 is in meters and t in seconds. Determine the total energy.

(I) A 1.28-kg mass oscillates according to the equation 𝓍 = 0.650 cos7.40 t where 𝓍 is in meters and t in seconds. Determine the kinetic energy and potential energy when 𝓍 = 0.260 m.

(I) If one oscillation has 3.0 times the energy of a second one of equal frequency and mass, what is the ratio of their amplitudes?

(II) What fraction of the total energy of a SHO is kinetic and what fraction potential when the displacement is one third the amplitude?