Question

An 8 kg body performs SHM of amplitude 30m.The restoring force is 60 N when the displacement when the displacement is 30 cm. Find a)Time period and acceleration b) Potential energy and kinetic energy when the displacement is 12 cm.

Answer 1

The potential energy is 144 J and kinetic energy is 756 J.

Explanation:

Mass of body "m" = 8 Kg

Amplitude "A" = 30 m

F = 60 N

Displacement "x" = 30 cm

F = - Kx

60 = - K (30)  => - K = 2

We know

ω = √ k / m

ω = √ 21 / 84 =  √ 1/4 = 1/2

T = 2π / ω  [ T = 2π /1/2 = 4π ]

a = A ω^2

a = 30 (1/2)^2

a = 30 / 4 = 7.5 m/s^2

P.E = 1/2 Kx^2 =  1/2 (2) x (12)^2 = 144 J

K.E =  1/2 K [ a^2 - x^2 ]

K.E = 1/2 x 2 x [(30)^2 - (12)^2 ]

K.E = ( 30 + 12 ) (30 - 12)

K.E = 42 x 18 =  756 J

Hence the potential energy is 144 J and kinetic energy is 756 J.

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Answer 2

Formulas used :

1)F=Kx

2)T=2pie under root m upon K

3) Acceleration =F/m or Kx/m

4)Potential energy =1/2kx2

5)K.E=1/2K(A2-x2)