Question

Derive the expression for the time period of oscillation of spring T= 2π√m÷√k, where T is the time period ,m is mass of the body and k is force constant
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Answer 1

Explanation:

Time period of a particle in SHM depends on the force constant k and mass m of the particle:

T=2π

k

m

. A simple pendulum executes SHM approximately. Why then is the time period of a pendulum independent of the mass of the pendulum?

(b) The motion of a simple pendulum is approximately simple harmonic for small angle oscillations. For larger angle of oscillation a more involved analysis shows that T is greater than 2π

g

l

. Think of a qualitative argument to appreciate this result.

(c) A man with a wristwatch on his hand falls from the top of a tower. Does the

watch give correct time during the free fall ?

(d) What is the frequency of oscillation of a simple pendulum mounted in a cabin that is freely falling under gravity ?