Question 248: Oscillations

Question

A mass attached to a spring performs S.H.M. whose displacement is $\mathrm{x}=3 	imes 10^{-3} \cos 2 \pi \mathrm{t}$ metre. The time taken to obtain maximum speed for the first time is

Accepted Answer

As the equation of displacement is given in terms of cosine, the particle starts from the extreme position.
Comparing the given equation with,
$$ \begin{array}{ll}  & x=A \cos (\omega t), \ & \omega=2 \pi \ 	herefore & \frac{2 \pi}{T}=2 \pi \ 	herefore & T=1 s . \end{array} $$
Now, velocity of the particle performing S.H.M. is maximum at the mean position. Thus, starting from extreme position, the time taken to reach the mean position for the first time is $\frac{\mathrm{T}}{4}$.
i.e., $\frac{1}{4}$ seconds.

Answer

$\frac{1}{12} \mathrm{~s}$

Answer

$\frac{1}{8} \mathrm{~s}$

Answer

$\frac{1}{4} \mathrm{~s}$

Answer

$\frac{1}{2} \mathrm{~s}$

Oscillations

A mass attached to a spring performs S.H.M. whose displacement is \mathrm{x}=3 \times 10^{-3} \cos 2 \pi \mathrm{t} metre. The time taken to obtain maximum speed for the first time is

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