Question

A block–spring system consists of a spring with constant k=425 N/m attached to a 2.00-kg block on a frictionless surface. The block is pulled 8.00 cm from equilibrium and released from rest. For the resulting oscillation, find the (a) ampli- tude, (b) angular frequency, (c) frequency, and (d) period. What is the maximum value of the block’s (e) velocity and (f ) acceleration?

Answer 1

a)
Amplitude is the maximum elongation of the spring,
A = 8.0 cm = 0.080 m

b)
Angular frequency, w = SQRT[k/m]
w= SQRT[425/2]
w= 14.58 rad/s

c)
Period, T = 2pi/w

T=6.28 / 14.58
= 0.43 s

d)
Frequency = 1/T

Frequency=1/0.43
Frequency= 2.32 Hz

e)
Maximum velocity = w A
= 14.58 * 0.08
= 1.17 m/s

f)
Maximum acceleration = w^2 A
= 14.58^2 * 0.08
= 17.006 m/s^2

I hope help you !!