Question

For a particle in SHM, the displacement x of the particle as a function of time t is given as x = A sin (2 pt) Here x is in cm and t is in seconds. Let the time taken by the particle to travel from x = 0 to x = A/2 be t and the time taken to travel from x = A/2 to x = A be t. Find t/t

• A. 44593
• B. 44621
• C. 44564
• D. 44563

Answer 1

Answer: (D)

44563

Answer 2

Here x = 0 at t = 0.
Also $\omega=\frac{2\pi}{T}=2\pi \quad\quad\quad \therefore T =1$ s
At t = t, x = A/2. Therefore,
A/2 = A sin (2pt)or 1/2 = sin (2pt)
$\therefore 2\pi t_{1}=\frac{\pi}{6} \quad\quad\quad\quad$ or $t_{1}=\frac{1}{12}s$
Time taken from x = 0 to x =A is $\frac{T}{4}=\frac{1}{4}s$
or $t_{1}+t_{2}=\frac{T}{4}=\frac{1}{4}s$
or $t_{2}=\frac{1}{4}-\frac{1}{12}=\frac{1}{6}s$
Hence $\frac{t_{1}}{t_{2}}=\frac{1/12}{1/6}=\frac{1}{2}.$