Question

$1)$ Displacement versus time curve for a particle executing $S.H.M.$ is shown in figure Identify the points marked at which



$A)$ velocity of the osillator is zero

$2)$ Displacement versus time curve for a particle executing $S.H.M.$ is shown in figure Identify the points marked at which


$B)$ speed of the oscillator is maximum

Answer 1

$A)$ From formula $v\left(x\right)=\omega \sqrt{A^2-x^2}$

$x=\pm A$

At extreme position (positive or negative) from mean position the velocity of the oscillator is zero.

Points $A,C,E$ and $G$ represents zero velocity points.

Final Answer: $\left(A\right),\left(C\right),\left(E\right),\left(G\right)$

$B)$ From formula $v\left(x\right)=\omega \sqrt{A^2-x^2}$

$x=0\left(\text{Mean position}\right)$

$v_{max}=\pm A\omega$

Speed

$\left|v_{max}\right|=A\omega$

At points $B,D,F$ and $H$ speed of the oscillator is maximum.

Final Answer: $\left(B\right),\left(D\right),\left(F\right),\left(H\right)$