A simple pendulum executing SHM with a period of 6 s between two extreme positions B and C about a point O. if the length of the arc BC is 10 cm, how long will the pendulum take the move from position C to a position D towards O exactly midway between C and O?

Options

A. 0.5 s
B. 1 s
C. 1.5 s
D. 3 s

Answer

B

Explanation

O is the mean position and B and C are extreme positions:
Given: BC=10cm
Since B and C are the extreme positions , therefore amplitude of the SHM oscillation is
`A=(BC)/(2)=5cm`
D is the midway between C and O.
`thereforeDC=(5)/(2)cm`
Since time is noted from extreme position, hence displacement x at any time t is, x=`Acosomegat`
For displacement CD, let `t_(1)` be the time taken. then
`(5)/(2)=5cosomegat_(1)`
`(1)/(2)=cosomegat_(1)` or `"cos"(pi)/(3)=cosomegat_(1)` or `t_(1)=(pi)/(3omega)`
`becauseomega=(2pi)/(T)=(2pi)/(6)=(pi)/(3)" "(becauseT=6s" (given)")`
`thereforet_(1)=1s`