First slide

Applications of SHM

Question

Restoring force on the bob of a simple pendulum of mass 100 g when its amplitude is 2° is(g=10m/ $s^{- 2}$ )

Moderate

A

0.017 N
B

1.7 N
C

0.17 N
D

0.0348 N

Solution

$\begin{array}{rcl} r e s t o r i n g f o r c e & = & F_{R} = m g \sin θ \\ m & = & m a s s o f o s c i l l a t o r, g = a c c e l e r a t i o n d u e t o g r a v i t y \\ i f θ i s v e r y s m a l l, t h e n \sin θ & ≃ & θ \\ t h e n F_{R} & = & m g θ \\ F_{R} & = & 100 (10^{- 3}) 10 (2^{0}) \\ F_{R} & = & \frac{2 π}{180} \\ F_{R} & = & \frac{2 \times 3.14}{180} \\ F_{R} & = & 0.0348 N \end{array}$

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