Please explain why each answer is correct a) When you use the approximation sin(
ID: 1871854 • Letter: P
Question
Please explain why each answer is correct
a) When you use the approximation sin(theta)=theta for a pendulum, you must specify the angle theta in radians only
b) Suppose you pull a simple pendulum to one side by an angle of 5°, let go, and measure the period of oscillation that ensues. Then you stop the oscillation, pull the pendulum to an angle of 10°, and let go. The resulting oscillation with have a period about the same as the period of the first oscillation
d) A grandfather clock is "losing" time because its pendulum moves too slowly. Assume that the pendulum is a massive bob at the end of a string. The motion of this pendulum can be sped up by shortening the string
c) At a playground, two young children are on identical swings. One child appears to be about twice as heavy as the other. If you pull them back together the same distance and release them to start them swinging, what will you notice about the oscillations of the two children? both children swing with the same period
Explanation / Answer
a) if theeta is very small then sin(theeta) is taken as theeta as sin(theeta) if theeta is small then the value is very small that can be approximated to theeta .
b) yes in both cases the period of oscillation will be approximately equal
c) we have time period T=2(pi)(l/g)^(1÷2)
So if we shorten string time period will decrease so we can speed up
d) both children will have same period as time T do not depend on mass from above relation