Question

When a particle executing SHM oscillates with a frequency ${}^{\prime }\omega {}^{\prime }$, then the kinetic energy of the particle

• A. Changes periodically with a frequency of ${}^{\prime }\omega {}^{\prime }$
• B. Changes periodically with a frequency of ${}^{\prime }2\omega {}^{\prime }$
• C. Changes periodically with a frequency of ${}^{\prime }\frac{\omega }{2}{}^{\prime }$
• D. Remains constant

Answer 1

The correct option is B Changes periodically with a frequency of ${}^{\prime }2\omega {}^{\prime }$

When the frequency of the SHM is $\omega$, the motion is represented as $x=Asin\omega t$.

Hence the kinetic energy of the motion is given as

$K=\frac{1}{2}m{v}^2$

$=\frac{1}{2}m\left(A\omega cos\right(\omega t){)}^2$

$=\frac{1}{2}m{A}^2{\omega }^{2}co{s}^2\left(\omega t\right)$

$=\frac{1}{2}m{A}^2{\omega }^2\left(\frac{cos2\omega t+1}{2}\right)$

which has frequency of $2\omega$.