Question

A child swings back and forth on a rope every 5s without significant damping taking place.

a. Create a position versus time graph of the child’s motion.

b. Create a velocity versus time graph of the same child’s motion that corresponds to the previous graph.

c. Create an acceleration versus time graph of the same child’s motion that corresponds to the previous graph.

d. Create a restoring force versus time graph of the same child’s motion that corresponds to the previous graph.

e. Would the first graph be considered a waveform or history graph? Explain why.

Answer 1

As the child is swinging back and forth.

we can say he is peforming oscillatory motion.

further we can assume he is performing Simple Harmonic Motion (S.H.M) for simplicity.

a) in S.H.M the relation between displace vs time is .

where A = maximum displace from mean postion, = angular frequency, = phase constant.

lets assume = 0. therefore, the equation for displacement will become .

it's corresponding graph will be :

b) on differentiation with respect to time, we get velocity as .

it's corresponding graph will be :

c) on further differention with respect to time, we get acceleration as

it's corresponding graph will be :

[note : acceleration is opposite to displacement]

d) the restoring force acts on the body is opposite to dispalce and is written as , where k = force constant.

its corresponding graph will be :

e) The first graph is a waveform as it is expressed as x = f(t).