Question

Assertion :In simple harmonic motion A is the amplitude of oscillation. If $t_1$ be the time to reach the particle from mean position to $\frac{A}{\sqrt{2}}$ and $t_2$ the time to reach from $\frac{A}{\sqrt{2}}$ to A, then $t_1=\frac{t_2}{\sqrt{2}}$
Reason : Equation of motion for the particle starting from mean position is given by $x=Acos\left(\omega t\right)$ and of the particle starting from extreme position is given by $Asin\left(\omega t\right)$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
• C. Assertion is correct but Reason is incorrect.
• D. Both Assertion and Reason are incorrect.

Answer 1

Answer: (D)

Both Assertion and Reason are incorrect.

From mean position to $\frac{A}{\sqrt{2}}$ time taken $t_1$
From $\frac{A}{\sqrt{2}}$ to mean position time taken $t_2$
This is incorrect as time takes should be same in both cases.
Second statement is also incorrect as equation of motion for a particle in simple harmonic motion is given by: $x\left(t\right)=Acos(\omega t+\varphi )$