An objects motion is described by the equation d4sinpit The

An object\'s motion is described by the equation d=4sin(pi*t). The displacement, d, is measured in meters. the time, t, is measured in seconds.

Part I: What is the object\'s position at t=0? Be sure to include appropriate units. Show work.

Part II: What is the object\'s maximum displacement from its resting position. Be sure to include appropriate units. Show work.

Part III: How much time is required for one oscillation? Be sure to include appropriate units. Show work.

Part IV: What is the frequency of this motion? Be sure to include appropriate units. Explain.

Part V: What will the height of the object be at t=1.75 seconds. Show work

Solution

d = 4sin(pi*t)

1) at t=0 ; d= 4sin(pi*0) =0 metres

2) Max. value of d = 4sin(pi*t) = 4metres at t= pi/2 seconds

3) One oscillation menas 1 time period.

Time period of d = 4sin(pi*t): T = 2pi/pi = 2 seconds

4) Frequency = 1/T = 1/2 per seconds = 0.5 per seconds

5) At t= 1.75sec

d = 4sin(pi*1.75) = -0.707 mt

Object is below the y axis at 0.707 mt