Question

Now Etienne and Hakim are ready to try a homework problem.

A 254 g block connected to a light spring with a force constant of k = 5 N/m is free to oscillate on a horizontal, frictionless surface. The block is displaced 6 cm from equilibrium and released from rest. Find the period of its motion. (Recall that the period, T, and frequency, f, are inverses of each other.)

_______ s

Determine the maximum acceleration of the block.

amax = ________ m/s^2

Answer 1

Mass of the block = m = 254 g = 0.254 kg

Force constant of the spring = k = 5 N/m

Amplitude of the oscillation = A = 6 cm = 0.06 m

Time period of motion = T

Time of a simple harmonic motion is given by,

T = 1.416 sec

Angular frequency of oscillation =

= 4.436 rad/s

Maximum acceleration of the block = a

a = A²

a = (0.06)(4.436)²

a = 1.18 m/s²

a) Period of motion = 1.416 sec

b) Maximum acceleration of the block = 1.18 m/s²