Question

If x, v and a denote the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period T, then which of the following do not change with time?

• A. $\frac{aT}{v}$
• B. $aT + 2 \pi v$
• C. $a^2 T^2 + 4 \pi^2 v^2$
• D. $aT$

Answer 1

Answer: (A)

$\frac{aT}{v}$

Answer 2

$\because$ In option (a), $\frac{a T}{v}=\frac{\frac{m}{s^{2}} \times s}{\left(\frac{m}{s}\right)}=\frac{m \times s^{2}}{m \times s^{2}}=\left[M^{0} L ^{0} T ^{0}\right]$
So, according to the result above relation does not depend on time. So, option (a) is correct.