[Year 12 Mechanics] Simple Harmonic Motion

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katsicum

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Hi, I have several questions for the following maths problem

A particle moving in Simple Harmonic Motion starts from rest at a distance 10 metres to the right of its centre of oscillation O. The period of the motion is 2 seconds.
i. Find the speed of the particle when it is 4 metres from its starting point. (answer v=8pi m/s)
i. Find the time taken by the particle to first reach the point 4 metres from its starting point, in seconds correct to 2 decimal places. (t=0.3s)

The first question is about part i). So my teacher told me that the simple harmonic motion form is x=10sin(pi*t). I don't quite understand why 10 is the amplitude. Why is it not x=asin(pi*t) - 10? Also for when it is 4 metres from its starting point, he subbed x=6 into the equation which made me very confused as to why x=6 not 4

Another question is for part ii). I have no idea how to solve it. Could someone please help me with this part?

Thank you!
 
katsicum said:
Hi, I have several questions for the following maths problem

A particle moving in Simple Harmonic Motion starts from rest at a distance 10 metres to the right of its centre of oscillation O. The period of the motion is 2 seconds.
i. Find the speed of the particle when it is 4 metres from its starting point. (answer v=8pi m/s)
i. Find the time taken by the particle to first reach the point 4 metres from its starting point, in seconds correct to 2 decimal places. (t=0.3s)

The first question is about part i). So my teacher told me that the simple harmonic motion form is x=10sin(pi*t). I don't quite understand why 10 is the amplitude. Why is it not x=asin(pi*t) - 10? Also for when it is 4 metres from its starting point, he subbed x=6 into the equation which made me very confused as to why x=6 not 4

Another question is for part ii). I have no idea how to solve it. Could someone please help me with this part?

Thank you!
Click to expand...
The question says:

.....starts from rest at a distance 10 metres to the right of its centre of oscillation O​

The origin is taken to be at O, which is 10 m away from the starting point.

At the stating point the speed of the particle is 0. It goes towards the origin and passes it and goes onto the left of the origin (remember the origin is the center of oscillation). So at what distance (left of the origin) from the origin the speed of the particle will become zero again?
 
Subhotosh Khan said:
The question says:

.....starts from rest at a distance 10 metres to the right of its centre of oscillation O​

The origin is taken to be at O, which is 10 m away from the starting point.

At the stating point the speed of the particle is 0. It goes towards the origin and passes it and goes onto the left of the origin (remember the origin is the center of oscillation). So at what distance (left of the origin) from the origin the speed of the particle will become zero again?
Click to expand...
Thank you for the help. I have been able to solve it myself
 
Why did x get replaced with 6 on only 1 side of the equation??
 
An equation has two sides. One side is to the left of the equal sign and the other side is to the right of the equal sign. In one of your equations you replaced x with 6 on the right hand side. Why?
 
Jomo said:
An equation has two sides. One side is to the left of the equal sign and the other side is to the right of the equal sign. In one of your equations you replaced x with 6 on the right hand side. Why?
Click to expand...
Hi, I see what you are referring to. I was doing in in a rush so the line "x=6" should have been since x=6 and then I should have subbed 6 into one side of the above equation but I took some shortcuts there. Sorry for the confusion :)))
 
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