A 2kg block hangs without vibrating at the bottom end of a spring with a force constant of 400 N/m. The top end of the spring is attached to the ceiling of an elevator car. The car is rising with an upward acceleration of 5 m/s 2 when the acceleration suddenly ceases at time t = 0 and the car moves upward with constant speed. (g = 10 m/s 2 )
(i) What is the angular frequency of oscillation of the block after the acceleration ceases?
Text Solution
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(i) Maximum extension the spring from natural position is x.
Then mg + ma = kx
⇒ x = 
= 7.5 cm
(ii) Extension of the spring when it is stretched to equilibrium line is x'.
mg =kx'
⇒ x' = 
= 5 cm
Therefore amplitude A = x –x' = 2.5 cm
(iii) If upward direction is taken as positive at t = 0, x = – A
Using x = A sin (ꞷt + φ )
– A = A sin φ
φ = 
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