Question

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

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

Answer 1

Answer: (D)

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