Question

Choose any 3 questions.

1.) What effect does N have on accurately determining the value of the period? What considerations keep one from allowing N to be very large, for example 1000?

2.) What does it mean for the pendulum to have a small angle? How far does the period (T) of the pendulum differ from the linear model that we used to describe the pendulum as a function of initial angle? Note that for this one you will need to measure the period of a single swing of the pendulum. How can you / did you do this?

3.) How can you investigate the pendulum under the effect of reduced gravity? How might you dilute the effect of gravity on the pendulum?

4.) What are the effects of air friction on the mechanical energy of the pendulum? Study the drop in amplitude of oscillation of the pendulum as a function of time, length, mass, period and initial amplitude.

5.) Define the terms amplitude, frequency, angular frequency, and period as they apply to the pendulum.

Answer 1

A simple pendulum may be described ideally as a point mass suspended by a massless string from some point about which it is allowed to swing back and forth in a place

Part 5

Amplitude - The maximum distance that the mass is displaced from its equilibrium position is defined as the amplitude of the oscillation.

Period - If a pendulum is set in motion so that is swings back and forth, its motion will be periodic. The time that it takes to make one complete oscillation is defined as the period T.

Frequency- The frequency f of the oscillations is the number of oscillations that occur per unit time and is the inverse of the period, f = 1/T

Angular Frequency- It is a measure of angular displacement given by where f is frequency.

Part 1

N is the number of oscillations that the pendulum is allowed each time for measurig time period. i.e

Time period = Time taken for N complete oscillations / N.

Sufficient value of N would allow value of time period to be measured precisely by averaging so that the result is minimally influenced by any practical error. Practical errors may include air blow in between, hands giving a shake or push to the pendulum etc. which might happen unknowingly in the experiments. A very large value of N is not advised since in such a case, the effect of air friction might effect our observations drastically. Also a large N would mean a large experimental time required.

Part 3

To investigate the effect of reduce gravity, we can use a metallic ball as pendulum bob and swing it below a magnet plate. The magnet plate would attract the ball to reduce the effect of gravity. Since simple pendulum's time period is given by

the time period will decrease under reduced gravity due to effective decrease in g.