Question

Find the velocity when KE = PE of the body undergoing SHM. Amplitude = x₀ and angular frequency is ω. How many times in a cycle KE = PE.

• A. $\frac{\omega x_{0}}{\sqrt{2}},2$
• B. ωx₀, 2
• C. $\frac{\omega x_{0}}{\sqrt{2}},4$
• D. ωx₀, 4

Answer 1

Answer: (C)

$\frac{\omega x_{0}}{\sqrt{2}},4$

Answer 2

$\frac{1}{2}m\omega^{2}\left( x_{0}^{2} - x^{2} \right) = \frac{1}{2}m\omega^{2}x^{2}$

or x = $\frac{x_{0}}{\sqrt{2}}$

V = ω$\sqrt{x_{0}^{2} - x^{2}} = \frac{\omega x_{0}}{\sqrt{2}}.$

This will be achieved 4 times in a cycle.