## Related questions with answers

An air-track glider attached to a spring oscillates between the 10 cm mark and the 60 cm mark on the track. The glider completes 10 oscillations in 33 s. What are the (a) period, (b) frequency, (c) angular frequency, (d) amplitude, and (e) maximum speed of the glider?

Solutions

Verified(a) When the object is oscillating about the origin, repeatedly going left and right by identical amounts it has a time period $T$ where the period $T$ is the time required for one complete oscillation or cycle. So, the given time $t=33$ s is the time required to complete $N=$ 10 cycles. In this case, the time period will be given by

$\begin{gather*} T = \dfrac{t}{N} \tag{1}\\ \end{gather*}$

Now, we plug the values for $t$ and $N$ into equation (1) to get $T$

$T = \dfrac{t}{N} = \frac{33 \mathrm{~s}}{10} = \boxed{3.3 \mathrm{~s}}$

The air-track glider oscillating on a spring is SHM.

(a)$\\$The time needed for one oscillation:

$T=\displaystyle \frac{33\mathrm{s}}{10\ oscillations}=3.3$ s/oscillation $=3.3\mathrm{s}$

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