Question

Average value of KE and PE over entire time period is

• A. $0,\frac{1}{2}m \, \omega ^{2}A^{2}$
• B. $\frac{1}{2}m \, \omega ^{2}A^{2},0$
• C. $\frac{1}{2}m \, \omega ^{2}A^{2}, \, \frac{1}{2}m \, \omega ^{2}A^{2}$
• D. $\frac{1}{4}m \, \omega ^{2}A^{2},\frac{1}{4}m \, \omega ^{2}A^{2}$

Answer 1

Answer: (D)

Maximum KE $=\frac{1}{2}m\omega ^{2}A^{2}$ ; minimum KE=0
Average KE $=\frac{0 + \frac{1}{2} m \omega ^{2} \, A^{2}}{2}=\frac{1}{4}m\omega ^{2}A^{2}$
Similarly average PE $=\left(\frac{0 + \frac{1}{2} m \left(\omega \right)^{2} \, A^{2}}{2}\right)$
$=\frac{1}{4}m\omega ^{2}A^{2}$
(average of $\text{sin}^{2} \theta $ and $\text{cos}^{2} \theta $ in a time period is $\frac{1}{2}$ )