Question

For a linear harmonic oscillator the force constant is 2 × 10⁶ N/m and total mechanical energy is 160 J.At some instant of time, its displacement is 0.01 m. Find its potential energy and kinetic energy at this position.

Answer 1

Answer:

Kinetic energy =  100J      

Potential energy = 160J

Explanation:

We have given,

$\text{A linear harmonic oscillator of force constant is }2\times 10^6 n/m$,

total mechanical energy=160 J,

displacement(a) =0.01m and

We have to find the potential energy and kinetic energy,

We know that,

Maximum potential energy = Total Mechanical energy = 160J

In a simple harmonic motion ,

$\text{kinetic energy} = \dfrac 12 Ka^2$

$\text{kinetic energy } = \dfrac 12 \times 2 \times 10^6 \times (0.01)^2\\\text{kinetic energy} = 10^2 = 100J$      

Kinetic energy =  100J