Question

A 240-g object attached to a spring oscillates on a frictionless horizontal table with a frequency of 4.00 Hz and an amplitude of 15.0 cm.

1) Calculate the maximum potential energy of the system.

2) Calculate the displacement of the object when the potential energy is one-half of the maximum.

3) Calculate the potential energy when the displacement is 10.0 cm.

Answer 1

step:1

Given that

mass m=0.24 kg

frequency f=4 hz

amplitude A=0.15 m

step:2

now we find the maximum potential energy of system

P.E max =1/2mw^2A^2=1/2*0.24*(2*3.14*4)^2*0.15^2=1.7 J

step:3

now we find the distance

P.E=1.7/2=0.85 J

0.85=1/2*0.24*(2*3.14*4)^2*x^2

displacement X=10.6 cm

step:4

now we find the potential energy

p.E=1/2*0.24*(2*3.14*4)^2*0.1^2=0.76 J