An objects motion is described by the equation d3cospit The

An object\'s motion is described by the equation d=3cos(pi/t). The displacement, d, is measured in meters. The time, t, is measured in seconds. Find (a) The object\'s position at t=0 (b)The object\'s maximum displacement from its resting position (c) The time required for one oscillation (d) The frequency

Solution

The given equation should be , d = 3*cos(pi*t)

a) at t= 0 , d = 3*cos(pi*0)

d = 3 m ( cos 0 ) = 1)

b) maximum displacement will be , when cos(theta) = 1

so d_max = 3m

c) d = 3*cos(pi*t)

in general , d = 3*cos(wt)

on comparing , w = pi

2*pi*f = pi

f (frequency) = 1/2 = 0.5 hz ( ans - d)

T(time period ) = 1/f

T = 2s