Question

Displacement vs. time curve for a particle executing $S.H.M.$ is shown in figure. Choose the correct statements.

• A. Phase of the oscillator is same at $t=2s$ and $t=6s.$
• B. Phase of the oscillator is same at $t=0s$ and $t=2s.$
• C. Phase of the oscillator is same at $t=1s$ and $t=7s.$
• D. Phase of the oscillator is same at $t=1s$ and $t=5s.$

Answer 1

Answer: (A), (D)

Phase of the oscillator is same at $t=1s$ and $t=5s.$

Simple harmonic motion: Simple harmonic motion, repetitive movement back and forth through an equilibrium, or central, position, so that the maximum displacement on one side of this position is equal to the maximum displacement on the other side.

In option $\left(a\right):$ From the figure the state at $t=0$ and $t=2$ are not the same as the displacement are not equal. So, the statement is incorrect.

In option $\left(b\right):$ From the figure the state at $t=2s$ and $t=6s$ are in the same state as the displacement and direction are the same. So, the statement is correct.

In option $\left(c\right):$ From the figure though the displacement is same at $t=1s$ and $t=7s$ but the direction is opposite. So, the statement is incorrect.

In option $\left(d\right):$ From the figure the state at $t=1s$ and $t=5s$ are in the same state as the displacement and direction are the same. So, the statement is correct.

Final Answer: Option (b), (d)