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Pendulum Simple Harmonic Motion Question

Hi Guys,

Stuck on a question, its probably a simple one but haven't had a question like this yet so I can't figure it out.

Here it is:

A pendulum oscillating at 30 times a minuet has an amplitude of 20cm. Released at maximum displacement, work out the displacement at
a) 0.5s
b) 0.75s

So I have worked out that the period is 2 and therefore the frequency is 0.5Hz, but not sure what to do next, any ideas?

Thanks,
Ben.

Reply 1

EricPiphany

Displacement is given as a cosine curve, Displacement = Amplitude * cos(2*pi*frequency * time)

x=A \cos(2 \pi ft)

I've chosen cosine instead of sine to simplify, because the motion starts at the maximum position.

(edited 8 years ago)

Reply 2

BenRichi_

Original post by EricPiphany

Displacement is given as a cosine curve, Displacement = Amplitude * cos(2*pi*frequency * time)

x=A \cos(2 \pi ft)

I've chosen cosine instead of sine to simplify, because the motion starts at the maximum position.

Thanks for your reply, I have tried to use this equation:

Displacement = 0.2 * cos(2*pi*0.5*0.5)

However the answer I get is 0.1999248434m but the sheet I'm working from says the answer is 0m so this is why I was confused?

Reply 3

EricPiphany

Original post by BenRichi_

Ye... change your calculator to radian mode when using these equation.
Or convert the argument to the cosine function into degrees by dividing by pi and multiplying by 180.

Reply 4

BenRichi_

Original post by EricPiphany

Ye... change your calculator to radian mode when using these equation.
Or convert the argument to the cosine function into degrees by dividing by pi and multiplying by 180.

Ah okay, thank you very much! I had a look back through some notes and it says to make sure to use the equations in radian mode as to avoid mistakes!

Thanks for the help!