Consider a simple harmonic motion of time period T. Calculate the time taken for the displacement to change value from half the amplitude to the amplitude.

T/6

*Since,* *the* *motion* *is* *a* *simple* *Harmonic.*

*Its* *equation* *will* *be* *given* *by* *the* *equation,*

*Now,* *for* *the* *first* *half* *journey,*

*we* *will* *get,*

*Φ* *=* *0,*

*In* *initial* *phase,*

*∴*

*For* *second* *Journey,* *from* *A/2* *to* *A,*

*Time* *taken* *from* *A/2* *to*

Now,

*∴*

*=T/6.*

1