Question

A mass is suspended from a vertical spring which is executing S.H.M. of frequency $5Hz$ . The spring is unstretched at the highest point of oscillation. The maximum speed of the mass is [acceleration due to gravity $g=10m{s}^{-2}$ ]

• A. $2\pi m{s}^{-1}$
• B. $\pi m{s}^{-1}$
• C. $\frac{1}{2\pi }m{s}^{-1}$
• D. $\frac{1}{\pi }m{s}^{-1}$

Answer 1

Answer: (D)

$T=2\pi \sqrt{\frac{m}{k}}$
$n=\frac{1}{2\pi }\sqrt{\frac{k}{m}}$
$25=\frac{1}{4{\pi }^2}\frac{k}{m}$
$k=100{\pi }^{2}m$
$kA=mg$
$A=\frac{mg}{k}$
$V_{\text{max}}=\omega A$
$=\frac{2\pi }{T}A$
$=2\pi nA$
$=\frac{2\pi \times 5\times mg}{k}$
$V_{\text{max}}=\frac{10\pi \times m\times 10}{100{\pi }^{2}m}=\frac{1}{\pi }m{s}^{-1}$