Question

In a lab experiment you observe that a pendulum swings with a “period” (time for one round trip) of $\mathbf{2}\mathbf{}\mathbf{s}$. In an iterative calculation of the motion, which of the following would NOT be a reasonable choice for $\mathbf{∆}\mathbf{t}$, for either hand or computer iterative calculations? a) $\mathbf{1}\mathbf{}\mathbf{s}$b) $\mathbf{0}\mathbf{.}\mathbf{1}\mathbf{}\mathbf{s}$c) $\mathbf{0}\mathbf{.}\mathbf{05}\mathbf{}\mathbf{s}$d) $\mathbf{0}\mathbf{.}\mathbf{01}\mathbf{}\mathbf{s}$.

Short answer

d)$0.01\mathrm{s}$ is not a reasonable choice for $∆\mathrm{t}$.

Step-by-step solution

Identification of the given data

The given data can be listed below as

• A pendulum is referred to as a weight that is hung from a fixed end for swinging freely.

• A constant force is applied to trigger the pendulum’s motion, which leads to imbalances in the equilibrium position of the pendulum.

• The swing time of the pendulum is the time taken by the pendulum to reach its starting destination after a whole swing.

• The pendulum swings at a period of $2\mathrm{s}$.

Determination of the unreasonable choice for the change in time

As the total period of the pendulum is $2\mathrm{s}$, the time$0.01\mathrm{s}$ will not be a reasonable choice for as this time is almost negligible for understanding the pendulum’s motion.

The other periods such as (a)$1\mathrm{s}$, (b)$0.01\mathrm{s}$and (c)$0.05\mathrm{s}$ can predict the time as the time is independent of the pendulum’s mass, plus these are not negligible. However, there are no devices that can predict the motion of a pendulum in this small amount of time, such as $0.01\mathrm{s}$.

Thus, d)$0.01\mathrm{s}$ is not a reasonable choice for $∆\mathrm{t}$.