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Numerical Problems on Oscillation

See here solved numerical problems included in the new course of Physics for Grade 11.

S.No Description of problem
Problem 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 the spring.
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Problem 2 A pendulum clock keeps perfect time at a location where the acceleration due to gravity is exactly 9.8 m-2. When the clock is moved to a higher altitude, it loses 80.0 s per day. Find the value of g at the new location.
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Problem 3 Calculate the length of a second pendulum having time period 2 seconds at a place where g = 9.8 ms-2.
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Problem 4 A body of mass m suspended from a spring with spring constant k vibrates with 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.
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Problem 5 A mass at the end of a spring describes SHM with a period of 0.04 s. Find the acceleration when the displacement is 0.04 m.
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Problem 6 A block weighing 4 kg extends a spring by 0.16 m from its un-stretched position. The block is removed and a 0.50 kg body is hung from same spring. If the spring is now stretched and released, what is its period of vibration?
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Problem 7 What should be the length of a simple pendulum whose time period is one second? What is its frequency?
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Problem 8 A spring whose spring constant is 80.0 N/m vertically supports a mass of 1.0 kg is at the 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 maximum velocity of one meter per second?
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Problem 9 800 g body vibrates SHM with amplitude 0.30 m. The restoring force is 60 N and the displacement is 0.30 m. Find out;
(i) T (ii) a (iii) v (iv) K.E (v) P.E, when the displacement is 12 cm.
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Problem 10 Find the amplitude, frequency and time period of an object oscillating at the end of a spring, if the equilibrium for its position at any instant t is given by x=0.25 cos⁡〖π/2 t〗.
Find the displacement of the object after 2.0 seconds.
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