Question

In a lab experiment you observe that a pendulum swings with a "period" (time for one round trip) of $2s$. In an iterative calculation of the motion, which of the following would NOT be a reasonable choice for $\Delta t$, for either hand or computer iterative calculations? a) $1\mathrm{s}$ b) $0.1\mathrm{s}$c) $0.05\mathrm{s}$ d)$0.01\backslash mathrm\{~s\}.$

Short answer

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

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 $0.01{\mathrm{s}}_{\text{will}}$not be a reasonable choice for $\Delta t$as this time is almost negligible for understanding the pendulum's motion.

The other periods such as $\left(\mathrm{a}\right)1\mathrm{s}$,(b) $0.1\mathrm{s}$and (c) $0.05\mathrm{s}$can predict the time $\Delta t$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 $\Delta t$.