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Springs

Two springs w...

Question

Two springs with negligible masses and force constant of $K_{1} = 200 N m^{- 1}$ and $K_{2} = 160 N m^{- 1}$ are attached to the block of mass $m = 10 k g$ as shown in the figure.Initially the block is at rest ,at the equilibrium position in which both springs are neither stretched nor compressed.At time $t = 0,$ a sharp impulse of $50 N s$ is given to the block with a hammer

Period of oscillations for the mass m is

\frac{π}{6} s

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Maximum velocity of the mass

m

during its oscillation is

10 m s^{- 1}

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Data are insufficient to determine maximum velocity

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Amplitude of oscillation is

0.83 m

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Solution

The correct option is A Period of oscillations for the mass m is $\frac{π}{6} s$
$K_{e f f} = K_{1} + K_{2}$
$K_{e f f} = (200 + 160) N m^{- 1} = 360 N m^{- 1}$
$F = - K_{e f f} x = 50 N$ , means, Ampletude of SHM $= x = \frac{50}{360} m$
$T = 2 π \sqrt{\frac{m}{K_{e f f}}} = 2 π \sqrt{\frac{10}{360}} = \frac{π}{3}$
$ω = \frac{2 π}{T} = \frac{2 π}{(\frac{π}{3})} = 6 r a d / s e c$
$v_{m a x} = ω x (a m p l i t u d e) = 6 \times \frac{5}{36} = \frac{5}{6} m s^{- 1}$
only"A" is correct.

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Similar questions

Two springs with negligible masses and force constants

k_{1} = 200 N / m

and

k_{2} = 160 N / m

are attached to the block of mass

m = 10 k g

as shown in the figure. Initially the block is at rest, at the equilibrium position in which both springs are neither stretched nor compressed. At time

t = 0 s

, sharp impulse of

50 N s

is given to the block with a hammer along the spring.

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The correct option is A Period of oscillations for the mass m is π6sKeff=K1+K2Keff=(200+160)Nm−1=360 Nm−1F=−Keffx=50 N, means, Ampletude of SHM =x=50360 mT=2π√mKeff=2π√10360=π3ω=2πT=2π(π3)=6 rad/secvmax=ωx(amplitude)=6×536=56 ms−1only"A" is correct.