Question

A metal cylinder with a mass of 3.50 kg is attached to a spring and is able to oscillate horizontally with negligible friction. The cylinder is pulled to a distance of 0.200 m from its equilibrium position, held in place with a force of 18.0 N,and then released from rest. It then oscillates in simple harmonic motion. (The cylinder oscillates along the x-axis, where

x = 0

is the equilibrium position.)

(a)

What is the spring constant (in N/m)?

N/m

(b)

What is the frequency of the oscillations (in Hz)?

Hz

(c)

What is the maximum speed of the cylinder (in m/s)?

m/s

(d)

At what position(s) (in m) on the x-axis does the maximum speed occur?

x = ±  m

(e)

What is the maximum acceleration of the cylinder? (Enter the magnitude in m/s².)

m/s²

(f)

At what position(s) (in m) on the x-axis does the maximum acceleration occur?

x = ±  m

(g)

What is the total mechanical energy of the oscillating spring–cylinder system (in J)?

J

(h)

What is the speed of the cylinder (in m/s) when its position is equal to one-third of the maximum displacement from equilibrium?

m/s

(i)

What is the magnitude of the acceleration of the cylinder (in m/s²) when its position is equal to one-third of the maximum displacement from equilibrium?

m/s²

Answer 1