1) When a pendulum 0.5m long swings back and forth, its angular displacement Ɵ from rest position, in radians is given by Ɵ=1/4sin((pi/2)t), where t is the time, in seconds. At what time(s) during the first 4 s is the pendulum displaced 1 cm vertically above its rest position? (assume the pendulum is at its rest position at 0).
I don't understand, the maximum is 0.25. Could someone solve with an explanation of the question?
You are correct that the maximum answer to that equation is 0.25. But i think you are incorrect in your assumptions about what that number is. That is an angle. Specifically 1/4th of a radian or about 14.32 degrees.
Look at this diagram:
The pendulum swings from point b to point d.
The forumla
This gives us:
Just remember that these angles are in radians and you should convert them to degrees by multiply by
L = .5m = ab = ad.
So we need to find ansuch that ed=.01m (1cm)
I will assume you can take it from here once you figure out cd then solve for theta
Then plug theta back into the original equation to find t
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