## F.Sc ICS Notes: Physics XI: Chapter 7 Oscillations Numerical Problems

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

**Numerical Problem 7.2:****A load of 15g elongates a spring by 2cm. If body of mass 294g is attached to the spring and is set into vibration with an amplitude of 10cm, what will be its (i) period (ii) spring constant (iii) maximum speed of its vibration.**

**Numerical Problem 7.3:****An 8 kg body executes SHM with amplitude 30cm. 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.

**Numerical Problem 7.4:****A block of mass 4kg is dropped from a height of 0.8m on to a spring of spring constant k = 1960 N/m, Find the maximum distance through which the spring will be compressed.**

**Numerical Problem 7.5:****A simple pendulum is 50cm long. What will be its frequency of vibration at a place where g = 9.8 m/s(2).**

**Numerical Problem 7.6:****A block of mass 1.6kg is attached to a spring with spring constant 1000n/m, as shown is figure on book 7.14. The spring is compressed through a distance of 2cm 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.**

**Numerical Problem 7.7:****A car of mass 1300kg is constructed using a frame supported by four springs. Each spring has a spring constant 20000N/m. If two people riding in the car have a combined mass of 160kg, find the frequency of vibration of the car, when it is driven over a pot hole in the road. Assume the weight is evenly distributed.**

__Find the amplitude, frequency and period of an object vibrating at the end of a spring, if the equation for its position, as a function of time, is:__

**Numerical Problem 7.8:**
x= 0.25 cos((pie/8)t) What is the displacement of the object after 2s?

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