# Shm question -- a mass hanging on a spring vertically set into motion

A mass on the end of a spring which is hanging vertically is raised up and let go. It then oscillates between 2m and 1.5m above the floor and completes 32 cycles in one minute. The height, h metres, of the mass above the floor after t seconds can be modelled by the function h=acos(pi t / 180) +c where a, b and c are constants.

(a) Determine exactly the period, T, of the oscillation in seconds per cycle and hence find the value of b.

(b) By considering the extremes of the oscillation, work out the values of a and c.

(c) Calculate exactly the value of h when t = 25 seconds.

(d) Find the first time when h = 1.75 metres.

(e) Sketch the graph of h against t for , labelling axes and critical values carefully.
For first part I have said frequency is 32/60 per sec
Period is 2pi/pi b/180 to give me b
Then I have said this is just shm moved up distance c so
Center is 2+1.5 /2 =1.75
Amplitude is .25 so A is .25
And at t=0 H=2=A+C giving me C

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haruspex
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h=acos(pi t / 180) +c where a, b and c are constants.
You missed b. Is it h=acos(pi b t / 180) +c?
For first part I have said frequency is 32/60 per sec
Period is 2pi/pi b/180 to give me b
OK, but giving you what value for b?
Center is 2+1.5 /2 =1.75
Amplitude is .25 so A is .25
Yes.

You missed b. Is it h=acos(pi b t / 180) +c?

OK, but giving you what value for b?

Yes.

To find b ill use frequency is 1/period
Are my conditions correct, ie H is 2 at t is 0?
Thanks

haruspex
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Gold Member
2020 Award