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.

7.9J

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3.5 x 10^-3J

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7.9 x 10^-3J

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35J

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Solution

The correct option is C
7.9 x 10^-3J

The total mechanical energy of the system is

$E = \frac{1}{2} m ω^{2} A^{2}$

$= \frac{1}{2} m {(\frac{2 π}{T})}^{2} A^{2} = \frac{2 π^{2} m A^{2}}{T^{2}}$

$= \frac{2 π^{2} (40 \times 10^{- 5} k g) (2.0 \times 10^{-} 2 m)^{2}}{(0.20 s)^{2}}$

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

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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.

The correct option is C 7.9 x 10-3J The total mechanical energy of the system is E=12mω2A2 =12m(2πT)2A2=2π2mA2T2 =2π2(40×10−5kg)(2.0×10−2m)2(0.20s)2 7.9×10−3J.