Question

Problem: A Physics student recorded the movement of a swinging pendulum for 10 s (seconds). The student began recording at the instant the pendulum was at its resting (vertical) position but moving to the right. The pendulum then moved right (positive displacement) and left (negative displacement) several times. The pendulum took 2 s to swing to the right and the left and then return to its resting position. The pendulum’s furthest distance to either side of vertical was 3 in. Graph the function that represents the pendulum’s displacement as a function of time. Answer each of the following questions for five points each.

A. Given that the experiment started when the swinging pendulum was at its vertical position (time = 0) what trig function would be the most obvious to use for the model? Also, what is the amplitude and period of the function?

B. Using your answers from A, above, write an equation that models the motion of the pendulum.

C. Graph at least two complete cycles of the function using your equation from B above.

Answer 1

(A) SINE function would be the most obvious to use for the model as the pendulum starts being timed at equilibrium position, this suggests you use a sine function since sin(0)=0. Also, A = |amplitude| ; distance from the midpoint =  3 in, T = period ; time it takes to make one full revolution = 2 s.

(B)

General wave function:

f(t) = A*sin( t*2/T - b) + c

where,

A = |amplitude| ; distance from the midpoint

T = period ; time it takes to make one full revolution

b = shifts the graph right/left

c = shifts the graph up/down

This graph lies right on the axis so there will be no need to shift the graph

f(t) = 3*sin(t*)

y-axis will be units of inches and x-axis, seconds

(C) graph: