August 19, 2019, 01:45:27 am

### AuthorTopic: application of calculus to the physical world  (Read 98 times) Tweet Share

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#### _.aliciaaa_

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##### application of calculus to the physical world
« on: June 23, 2019, 04:30:26 pm »
0
I need help with this question,

A particle is oscillating in simple harmonic motion such that its displacement x metres from a given origin
O satisfies the equation d^2 x / dt^2= -4x  , where t is the time in seconds.

a. Show that x = a cos(2t + ) is a possible equation of motion for this particle, where a and  are
constants.
b. The particle is observed at time t = 0 to have a velocity of 2 metres per second and a
displacement from the origin of 4 metres. Show that the amplitude of oscillation is 17 metres.
c. Determine the maximum velocity of the particle.

#### RuiAce

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##### Re: application of calculus to the physical world
« Reply #1 on: June 23, 2019, 04:45:41 pm »
+1
Specifically which part are you requesting help for?

#### _.aliciaaa_

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##### Re: application of calculus to the physical world
« Reply #2 on: June 23, 2019, 04:49:52 pm »
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the whole thing  :/

#### RuiAce

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##### Re: application of calculus to the physical world
« Reply #3 on: June 23, 2019, 05:28:02 pm »
+1
If you require further help, you should post any understanding at all you have of the problem. That way, we can tailor it more to what you actually require. For now, here are some hints.

a) Differentiate it twice and then pull out the relevant constant as a factor. This is a very common question in the exam and is free marks in the long run.
b) Rely on the equation in part a) to do this part. There may be some simultaneous equations to solve. (Alternatively, you could use $v^2=n^2(a^2-x^2)$ if you prefer, but I haven't checked that it will work using this approach.)
c) For trigonometric functions, the maximum value of $\sin x$, $\cos x$, $-\sin x$ and $-\cos x$ are 1, which you can assume and use here.