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  •  A  collar is attached to a spring of spring constant. <img alt="900 \mathrm{~N}

 A 9 \mathrm{~kg} collar is attached to a spring of spring constant. 900 \mathrm{~N} / \mathrm{m}. It slides without friction over a horizontal rod. The collar is displaced from its equilibrium

Position by 20 \mathrm{~cm} and released.

Calculate

(a) The Period of oscillation

(b) The maximum speed

(c) maximum acceleration of the collar.

Option: 1

T=0.63 sec, V_{max}=2m/s,amax=20m/s^2


Option: 2

T=0.64 sec, V_{max}=2m/s,amax=30m/s^2


Option: 3

T=0.64 sec, V_{max}=3m/s,amax=20m/s^2


Option: 4

T=0.63 sec, V_{max}=5m/s,amax=20m/s^2


Answers (1)

best_answer

(a)

\begin{aligned} & T=2 \pi \sqrt{\frac{m}{K}}=2 \pi \sqrt{\frac{9}{900}}=\frac{2 \pi}{10} \\ & T=\frac{2 \times 3.14}{10}=0.63 \mathrm{sec} . \\ & T=0.63 \mathrm{sec} . \end{aligned}

(b)

\begin{aligned} & V_{\max }=A w \\ & \frac{20}{100} \times \sqrt{\frac{K}{m}} \\ & \frac{20}{100} \times \sqrt{\frac{900}{9}} \\ & \frac{20}{100} \times \sqrt{100} \\ & \frac{20}{100} \times 10=\frac{200}{100}=2 \mathrm{~m} / \mathrm{s} \\ & V_{\text {max }}=2 \mathrm{~m} / \mathrm{s} \end{aligned}

(c)

\begin{aligned} &\operatorname{amax}=\omega^2 A\\ &\begin{aligned} & \frac{K}{m} \times A \\ & \frac{900}{g} \times \frac{20}{100}-20 \mathrm{~m} / \mathrm{s}^2 \\ & a \max =20 \mathrm{~m} /\mathrm{~s}^2 \end{aligned} \end{aligned}

 

Posted by

himanshu.meshram

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