# Science

A body weighing 150 N, moves with simple harmonic motion. The velocity and
acceleration of the body when it is 200 mm from the centre of oscillation, are 5 m/s
and 20 m/s2 respectively.Determine (a) amplitude of motion ,no. of vibrations per minute, Periodic time and angular velocity

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1. mass = 150/g or about 15 kg but who needs it?

x = A sin w t
v = Aw cos wt
a = -Aw^2 sin wt = -w^2 x
=============================
when
x = .2 = A sin w t
v = 5 = Aw cos w t
a = +20=+Aw^2 sin w t = +w^2x
===============================
so
w^2 x = w^2(.2) = 20
w^2 = 200/2 = 100

now rewrite
.2 = A sin 10 t
5 = 10 A cos 10t
20 = 100A sin 10t

.2 = A sin 10 t
.5 = A cos 10 t

.04 = A^2 sin^2 10 t
.25 = A^2 cos^2 10 t

.04/A^2 + .25/A^2 = sin^2+cos^2 = 1

A^2 = .29

I guess you can take it from there
remember w = 2 pi f = 10
so f = 5/pi

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