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Chapter 8: Q. 39 (page 555)

An object attached to a coiled spring is pulled down a distance a = 3 units from its rest position and then released. Assuming that the motion is simple harmonic with period T = 4 seconds, develop a model that relates the displacement d of the object from its rest position after t seconds. Also assume that the positive direction of the motion is up.

Short Answer

Expert verified

The required equation isd=3sinπt2.

Step by step solution

01

Step 1. Given Information

The value ofais 3 units and the time period is 4 seconds.

02

Step 2. Find ω

  • Time period is equal to 2πω.
  • Equate this to 4 and find the value of ω.

2πω=4ω=π2

03

Step 3. Create the equation of motion.

  • Substitute a=3,ω=π2into d=asinωtand find the equation of motion.

d=3sinπ2t.

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