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Chapter 8: Q. 40 (page 555)

In Problems 40 and 41, the distance d (in feet) that an object travels in time t (in seconds) is given.

(a) Describe the motion of the object.

(b) What is the maximum displacement from its rest position?

(c) What is the time required for one oscillation?

(d) What is the frequency?

d=6sin2t

Short Answer

Expert verified

(a) The motion is harmonic.

(b) Maximum distance covered from initial position is 6 feet.

(c) Time period to cover one oscillation is 蟺seconds.

(d) The frequency islocalid="1646895030365" 1蟺

Step by step solution

01

Part (a) Step 1. Given Information

The equation of distance with respect to time isd=6sin2t.

02

Part (a) Step 2. Compare the Equation with Equation of Harmonic Motion

  • The equation of simple harmonic motion is d=asin蝇t.
  • The given equation is same as this equation with a=6,蝇=2
  • So, the motion of the object is simple harmonic motion.
03

Part (b) Step 1. Given Information

The equation of distance isd=6sin2t.

04

Part (b) Step 2. Find Maximum Distance from starting position

  • The maximum distance isa.
  • Here, a=6.
  • So, the maximum distance is 6 feet.
05

Part (c) Step 1. Given Information

The given equation of distance isd=6sin(2t).

06

Part (c) Step 2: Find the Time Period of 1 Oscillation

  • The time period is given by 2蟺蝇.
  • Here, 蝇=2.
  • So, the time period of one oscillation is2蟺2=蟺
07

Part (d) Step 1: Given Information

The equation of distance covered by the object is d=6sin(2t).

08

Part (d) Step 2: Find Frequency

  • The frequency is given by the reciprocal of the time period of one oscillation.
  • So, the frequency is f=1蟺oscillation per seconds.

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Find the area of the triangle. Round answer to two decimal places.

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