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 the x axis between turning points at x1 = 105 cm and x2 = 175 cm. (a) At which of the following positions does the particle have maximum speed? a.105 cm b.122.5 cm c.140 cm d.some other position e.The same greatest value occurs at multiple points. (b) At which position does it have maximum acceleration? a.105 cm b.122.5 cm c.140 cm d.some other position e.The same greatest value occurs at multiple points. (c) At which position is the greatest net force exerted on the particle? a.105 cm b.122.5 cm c.140 cm d.some other position e.The same greatest value occurs at multiple points. (d) At which position does the particle have the greatest magnitude of momentum? a.105 cm b.122.5 cm c.140 cm e.some other position d.The same greatest value occurs at multiple points. (e) At which position does the particle have the greatest kinetic energy? a.105 cm b.122.5 cm c.140 cm d.some other position e.The same greatest value occurs at multiple points. (f) At which position does the particle-spring system have the greatest total energy? a.105 cm b.122.5 cm c.140 cm d.some other position e.The same greatest value occurs at multiple points.

Explanation / Answer

A mass–spring system moves with simple harmonic motion along the x axis between turning points at x1 = 17 cm and x2 = 86 cm.

1. At which position does the particle have the greatest magnitude of momentum?
a. 17 cm
b. 43 cm
c. 51.5 cm
d. some other position
e. The greatest value occurs at multiple points.

2. At which position does the particle have greatest kinetic energy?
a. 17 cm
b. 43 cm
c. 51.5 cm
d. some other position
e. The greatest value occurs at multiple points.

3. At which position does the particle–spring system have the greatest total energy?
a. 17 cm
b. 43 cm
c. 51.5 cm
d. some other position
e. The greatest value occurs at multiple points.

A mass–spring system moves with simple harmonic motion along the x axis between turning points at x1 = 17 cm and x2 = 86 cm.

1. At which position does the particle have the greatest magnitude of momentum?
The velocity and hence the momentum is the maximum at the equilibrium position .(center position)
(86 +17)/2 = 51.5 cm


2. At which position does the particle have greatest kinetic energy?
The velocity and hence the K.E is the maximum at the equilibrium position. (Center position)
c. 51.5 cm

3. At which position does the particle–spring system have the greatest total energy?
At all points the total energy remains the same and hence there is no correct answer to choose from.

Probably, e is the nearest answer.

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