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

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

$E_P=\frac{1}{2}kx^2$

$E_P=600\times 0.01=6 J$

$E_K=\frac{1}{2}mv^2$

$E_K=\frac{1}{2}\times 3\times 3^2=13.5 J$

$E_T=13.5+6=19.5 J$

When mass reaches amplitude its velocity becomes zero

there is only potential energy which is equal to Total energy

$E_T=E_P=19.5 J$