A body of mass 1 kg is executing simple harmonic motion. Its displacement x (in cm) at time t (in second) is given by x = 6 s i n ( 100 t + π 4 ) The maximum kinetic energy of the body is Options: A . &nbsp6 J B . &nbsp18 J C . &nbsp24 J D . &nbsp36 J

Answer: Option B : B Velocity of the body at time t is v = d x d t = ( 6 × 100 ) c o s ( 100 t + π 4 ) c m s − 1 ∴ V m a x = 600 c m s − 1 = 6 m s − 1 Maximum KE 1 2 m v 2 m a x = 1 2 × 1 × ( 6 ) 2 = 18 J Hence the correct choice is (b)

A body of mass 1 kg is executing simple harmonic motion. Its displacement

Question

A body of mass 1 kg is executing simple harmonic motion. Its displacement x (in cm) at time t (in second) is given by

x = 6 s i n (100 t + \frac{π}{4})

The maximum kinetic energy of the body is

Options:

A . 6 J

B . 18 J

C . 24 J

D . 36 J

Answer: Option B
:
B
Velocity of the body at time t is

v = \frac{d x}{d t} = (6 \times 100) c o s (100 t + \frac{π}{4}) c m s^{- 1}

∴ V_{m a x} = 600 c m s^{- 1} = 6 m s^{- 1}

Maximum KE

\frac{1}{2} m v_{m a x}^{2} = \frac{1}{2} \times 1 \times (6)^{2} = 18 J

Hence the correct choice is (b)

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