Question

A particle of mass 40 g executes a simple harmonic motion of amplitude 2.0 cm. If the time period is 0.20 s, find the total mechanical energy of the system.

• A. 7.9J
• B. 3.5 $\times$ 10${}^{-3}$J
• C. 7.9$\times$ 10${}^{-3}$J
• D. 35J

Answer 1

The correct option is C

7.9$\times$ 10${}^{-3}$J

The total mechanical energy of the system is

$E=\frac{1}{2}m{\omega }^2{A}^2$

$=\frac{1}{2}m{\left(\frac{2\pi }{T}\right)}^2{A}^2=\frac{2{\pi }^{2}m{A}^2}{T^2}$

$=\frac{2{\pi }^2(40\times {10}^{-5}kg)(2.0\times {10}^{-}2m{)}^2}{(0.20s{)}^2}$

$7.9\times {10}^{-3}J.$