A particle executes SHM of type x-asin- t- It takes time t1 from x-0 to x-a2 and t2 from x-a2 t2 from x-a2 to x-a- The ratio of t1-t2 will be-

A particle executes simple harmonic motion between x = -A and x=+ A. The time taken for it to go from the mean position, O to $\frac{A}{2}$ is $T_{1}$ and to go from $\frac{A}{2}$ to A is $T_{2}$ . Then,

Q. A particle executes simple harmonic motion between x = -A and x = +A. The time taken for it to go from 0 to A/2 is

T_{1}

and to go from A/2 to A is

T_{2} .

Then

Q. A particle executes simple harmonic motion (amplitude

= A

) between

x = - A

and

x = + A

. The time taken for it to go from

0

\frac{A}{2}

T_{1}

and to go from

\frac{A}{2}

A

T_{2}

. Then

Join BYJU'S Learning Program

A particle executes SHM of type x=asinωt. It takes time t1 from x=0 to x=a2 and t2 from x=a2 t2 from x=a2 to x=a. The ratio of t1:t2 will be:

The correct option is B 1:2By symmetry the time period from a=0 to a=a is T/4. Let eliminate the options the time taken at extreme i.e. at n=a the time taken is more at extreme than at mid position so t2>t1a2=asinwt1⇒wt1=π6⇒t1=π6×T2π=T12t2=T4−T12=T6t2t1=12

A particle executes SHM of type $x = a s i n ω t$ . It takes time $t_{1}$ from $x = 0$ to $x = \frac{a}{2}$ and $t_{2}$ from $x = \frac{a}{2}$ $t_{2}$ from $x = \frac{a}{2}$ to $x = a$ . The ratio of $t_{1} : t_{2}$ will be: