A particle on a spring moves in simple harmonic motion along the x axis between

Question

A particle on a spring moves in simple harmonic motion along thex axis between turning points at x1 =115 cm and x2 =150 cm. (a) At which of the followingpositions does the particle have maximum speed?
1 115cm
123.75cm    
132.5cm
some other position
The same greatest value occurs at multiplepoints.


(b) At which position does it have maximum acceleration?
2 115cm
123.75cm    
132.5cm
some other position
The same greatest value occurs at multiplepoints.


(c) At which position is the greatest net force exerted on theparticle?
3 115cm
123.75cm    
132.5cm
some other position
The same greatest value occurs at multiplepoints.


(d) At which position does the particle have the greatest magnitudeof momentum?
4 115cm
123.75cm    
132.5cm
some other position
The same greatest value occurs at multiplepoints.


(e) At which position does the particle have the greatest kineticenergy?
5 115cm
123.75cm    
132.5cm
some other position
The same greatest value occurs at multiplepoints.


(f) At which position does the particle-spring system have thegreatest total energy?
6 115cm
123.75cm    
132.5cm
some other position
The same greatest value occurs at multiplepoints.

1 115cm
123.75cm    
132.5cm
some other position
The same greatest value occurs at multiplepoints.
1 115cm
123.75cm    
132.5cm
some other position
The same greatest value occurs at multiplepoints.
1 2 115cm
123.75cm    
132.5cm
some other position
The same greatest value occurs at multiplepoints.
2 115cm
123.75cm    
132.5cm
some other position
The same greatest value occurs at multiplepoints.
2 3 115cm
123.75cm    
132.5cm
some other position
The same greatest value occurs at multiplepoints.
3 115cm
123.75cm    
132.5cm
some other position
The same greatest value occurs at multiplepoints.
3 4 115cm
123.75cm    
132.5cm
some other position
The same greatest value occurs at multiplepoints.
4 115cm
123.75cm    
132.5cm
some other position
The same greatest value occurs at multiplepoints.
4 5 115cm
123.75cm    
132.5cm
some other position
The same greatest value occurs at multiplepoints.
5 115cm
123.75cm    
132.5cm
some other position
The same greatest value occurs at multiplepoints.
5 6

Explanation / Answer

I know that for the maximum momentum, kinetic energy, the particle would be at its equilibrium position, so (115 +150)/2 = 132.5

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