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 $\frac{1}{2}$ )