Question

a mass of 0.7kg is attached to a horizontal spring (k=5.2) the spring is compressed to 20cm and released . assume that the spring is ideal and frictionless and the mass oscillates horizontally, 1.what is the amplitude of oscillation
2.what is the maximum speed
3.what are the speed and acceleration of the mass when its displacement is at 12cm

Answer 1

1.
Max. compression is 20cm - so the amplitude A is 0.2m.

2.(1/2)mV^2 = (1/2)kA^2
V^2 = kA^2/m = 5.2*0.04/0.7
V=0.54m/s

3.Speed at X = sqrt(k/m)sqrt(A^2-X^2)
=2.72sqrt(.04-0.0144)
= 2.72*0.16= 0.43m/s

Acc. at X= (k/m)x= (5.2/0.7)*0.12
=0.89 m/s^2