Numerical Problems 7.1: A 100 g body hung on a spring, which elongates the spring by 4 cm. When a certain object is hung on the spring and set vibrating, its period is 0.568 s. What is the mass of the object pulling the spring? (Ans: 0.20 kg)

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Numerical Problems 7.2: A load of 15 g elongates a spring by 2 cm. If body of mass 294 g is attached to the spring and is set into vibration with an amplitude of 10 cm, what will be its (i) period (ii) spring constant (iii) maximum speed of its vibration. (Ans: (a) 1.26 s, (b) 7.35 N m⁻¹, (c) 49.0 cm s⁻¹)

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Numerical Problems 7.3: An 8 kg body executes SHM with amplitude 30 cm. The restoring force is 60 N when the displacement is 30 cm. Find.

(i) Period.
(ii) Acceleration, speed, kinetic energy and potential energy when the displacement is 12cm. 

(Ans: (i) T = 1.3 s (ii) `\vec a` = 3 m s⁻² , `\vec v` = 1.4 m s , K.E = 7.6 J , PE = 1.44 J) )

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Numerical Problems 7.4: A block of mass 4 kg is dropped from a height of 0.8 m on to a spring of spring constant k = 1960 N m⁻¹, Find the maximum distance through which the spring will be compressed. (Ans: 0.18 m)

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Numerical Problems 7.5: A simple pendulum is 50 cm long. What will be its frequency of vibration at a place where g = 9.8 m s⁻². (Ans: 0.70 Hz)

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Numerical Problems 7.6: A block of mass 1.6 kg is attached to a spring with spring constant 1000 N m⁻¹, as shown is figure on book 7.14. The spring is compressed  through a distance of 2 cm and the block is released from rest. Calculate the velocity of the block as it passes through the equilibrium position, x = 0, if the surface is frictionless. (Ans: 0.50 m s⁻¹)



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