Easy Physics Question for 10 points?

Question

A frictionless block of mass 1.95 kg is attached to an ideal spring with force constant 310 N/m. At t=0 the spring is neither stretched nor compressed and the block is moving in the negative direction at a speed of 12.6 m/s.

Find the amplitude.

Find the phase angle.

Answer 1

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Mass =m =1.95 kg

Force constant = k =310 N/m

At t=0 the spring is neither stretched nor compressed means block is at mean position

The block is moving in the negative direction means half cycle is completed, half of Period is over means phase angle is pi

At mean position speed is maximum

Maximum speed = Vm =Aw=12.6 m/s

where A is amplitude and w is angular frequency.

w= sq rt k/m =310 /1.95 = sq rt 158.974 = 12.6085 rad/s

Aw=12.6 m/s

A =12.6 /12.6085=0.9993 m

The amplitude is 0.9993 m

The phase angle = pi =180 degree
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Answer 2

At t=0 all of the energy is kinetic:

E = 1/2 m v^2

When the spring is fully extended, all of the energy is potential:

E = 1/2 k A^2

Set these two expressions for E equal and solve for the amplitude.

Since the mass is moving in the negative direction at t=0, your phase angle is π ( or 180 degrees ).

Answer 3

Yeah, as you say, an easy question. Shouldn't cause you any problems at all.

Why do you need to find the phase angle? Have you lost it?