**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.

**Problem 2:** A body of mass 0.025 kg attached to a spring is displaced through 0.1 m to the right of the mean position. If spring constant is 0.4 N/m and its velocity at the end of this displacement be 0.4 m/s, calculate

(1) Time period (2) Frequency (3) Angular speed

(4) Total energy (5) Amplitude (6) Max velocity

(7) Maximum acceleration

**Problem 3:** A simple pendulum completes one vibration in one second. Calculate its length when g = 9.8 m/s^2.

**Problem 4:** Calculate the length of a second pendulum having time period 2 s at a place where g = 9.8 m/s^2.

**Problem 5:** A body of mass ‘m’ suspended from a spring with force constant k vibrates with ‘f1’. When this length is cut into half and the same body is suspended from one of the halves, the frequency is ‘f2’. Find f1/f2.

**Problem 6:** A mass at the end of a spring describes S.H.M with T = 0.40 s. Find out **a **when the displacement is 0.04 m?

**Problem 7:** A block weighing 4.0 kg extends a spring by 0.16 m from its un-stretched position. The block is removed and a .50 kg body is hung from the same spring. If the spring is now stretched and then released, what is its period of vibration?

**Problem 8:** What should be the length of simple pendulum whose time period is one second? What is its frequency?

**Problem 9:** A spring whose spring constant is 80.0 N/m vertically supports a mass of 1.0 kg is at rest. 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 meter per second?

**Problem 10:** A 8000 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 (i) T (ii)** a** (iii) **v** (iv) K.E (v) P.E when the displacement is 12 cm.

**Problem 11:** Find the amplitude, frequency and time period of an object oscillating at the end of spring, if the equation for its position at any instant t is given by x = .5cos(pi/8)t. Find the displacement of the object after 2 s.

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