Question

A spring is suspended under gravity with a block attached to it. The block oscillates in the vertical plane according to $x=asinwt$ with time period $8$ seconds. The ratio of velocities of the particle at $t=1$ sec to $t=3$ sec is

• A. 2 : 1
• B. 1 : 1
• C. 3 : 4
• D. 2 : 3

Answer 1

Answer: (B)

1 : 1

$x=asin\omega t$
$V=\frac{dx}{xt}=a\omega cos\omega t$
$T=\frac{2\pi }{\omega };\omega =\frac{2\pi }{T}=\frac{\pi }{4}\frac{rad}{sec}$
$\frac{V_1}{V_2}=\frac{cos\omega t_1}{cos\omega t_2}=\frac{cos\frac{\pi }{4}}{cos\frac{3\pi }{4}}=\frac{1}{1}$