Question

A 3-kg object is attached to a spring and moving in simple harmonic motion. Its angular frequency is 20 rads/sec. When the mass-spring system is 0.10 m from its equilibrium position it has a velocity of v=3 m/s. What is the potential energy when the mass reaches amplitude? A. 0 J

B. 6 J
C. 13.5 J
D. 8 J
E. 19.5 J

Answer 1

Answer:19.5 J

Step-by-step explanation:

Given

mass of block=3 kg

angular frequency=20 rad/sec

spring constant
`k=\omega _n^2m=1200 N/m`

we know total energy remain conserved

`E_T at x=0.1 m`

`E_T=E_P+E_K`

Where
`E_K`=kinetic energy

`E_P`=potential Energy

`E_P=(1)/(2)kx^2`

`E_P=600* 0.01=6 J`

`E_K=(1)/(2)mv^2`

`E_K=(1)/(2)* 3* 3^2=13.5 J`

`E_T=13.5+6=19.5 J`

When mass reaches amplitude its velocity becomes zero

there is only potential energy which is equal to Total energy

`E_T=E_P=19.5 J`