# Equivalent length of simple pendulum,converted from compound pendulum - Theory of Machines - 1

Q.  What is the equivalent length of simple pendulum, when compound pendulum is converted into simple pendulum?
- Published on 06 Aug 15

a. le = (k + l ) / l
b. le = l2 / (k2 + l2)
c. le = (k2 + l2) / l
d. none of the above

ANSWER: le = (k2 + l2) / l

#### Discussion

• Sravanthi   -Posted on 19 Oct 15
Compound pendulum

- A rigid body is known as compound pendulum, if it oscillates with small amplitude under the action of gravity force.

Frequency of oscillations = (1 / 2π) √(g l / k2 +l2) Hz --------------------- (1)

Simple pendulum

- A simple pendulum is formed if a heavy bob is suspended vertically by using an inextensible weightless string.

Frequency of oscillations = (1 / 2π) √(g / l) Hz ----------------------------- (2)

The equivalent length of simple pendulum, when compound pendulum is converted into simple pendulum is given by comparing equation (1) and (2),

Therefore, le = (k2 + l2) / l

le = (k2 / l) + l

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