1: A force of 0.4 N is required to displace a body attached to a spring through 0.1 m from its mean position. Calculate the spring constant of spring. (k = 4 N m⁻¹)

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2: A pendulum clock keeps perfect time at a location where the acceleration due to gravity is exactly 9.8 m s⁻². When the clock is moved to a higher altitude, it loses 80.0 s per day. Find the value of g at this  new location. (9.78 m s⁻²) 



3: Calculate the length of a second; pendulum having time period 2 s at a plate where g = 9.8 m s⁻². (L = 0.992 m)

4: A body of mass 'm', suspended from a spring with force constant k, vibrates with frequency 'f₁ ' When its length is cut into half and the same body is suspended from one of the halves, the frequency is 'f₂'. Find out f₁ f₂⁻¹. (f₁ f₂⁻¹  = 0.707)

5: A mass at the end of spring describes S.H.M with T = 0.40 s. Find out `\vec a` when the displacement is 0.04 m. (a = -9.86 m s⁻² approx) 

6: A block weighing 4.0 kg extends a spring by 0.16 m from its upstretched position. The block is removed and a 0.50 kg body is hung from same spring. If the spring is now stretched and then released, what is its period of vibration? (T = 0.28 )



7: What should be the length of simple pendulum whose time period is one  second? What is its frequency? ((1) = 0.25 m (ii) f = 1 cps)

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8: A spring, whose spring constant is 80.0 N m⁻¹ vertically supports a mass  of 1.0 kg is at rest position. Find the distance by which the mass must be pulled down, so that on being released, it may pass the mean position with velocity of one metre per second. (x₀ = 0.11)



9: A 800 g body vibrates S.H.M with amplitude 0.30 m. The restoring force is 60 N and the displacement is 0.30 m. Find out (1) T (ii) `\vec a` (iii) `\vec v` (iv) K.E (v) P.E when the displacement is 12cm.

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10: Find the amplitude, frequency and time period of an object oscillating at the end of a spring, if the equation for its position at any instant given by x = 0.25 cos`(\ frac {Ï€}{8})` t . Find the displacement of the object after 2 s. (0.25 m, `\ frac {1}{16}`Hz, 0.18 m)


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