Simple harmonic motion question

In summary, the time it takes the object to go from 0.32m to 0.16m is 0.15 seconds and the time it takes to go from 0.16m to 0 is 0.075 seconds.
  • #1
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Homework Statement



An object undergoing SHM with a period 0.9s and amplitude of 0.32 m at t=0 the object is at 0.32 m and is instantaneously at rest. Calculate the time it takes the object to go a) from 0.32 to 0.16 m
b) from 0.16 m to 0

i can do a but don't understand why when i do the calculation x is not -1/2 and is 1/2

Homework Equations


x=Asin(wt)




The Attempt at a Solution



so for first part 1/2 = 0.32 cos (2+2/9)*pi * t

i get 0.15 correct answer and for part b i do the same thing because it is the same distance excpt i shift the graph so t1 is at 0.16 like this 0.16 = a cos ((wt) - pi/4)
 
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  • #2
If 0.15s is the correct value for the time to reach 0.16m from 0.32m, then to reach 0 from 0.32m is the time for exactly one quarter of a period. (=0.9s/4)
The time from 0.16m to zero is then just the time for the quarter period minus your first answer.
 

Related to Simple harmonic motion question

1. What is simple harmonic motion?

Simple harmonic motion is a type of periodic motion where an object moves back and forth around a stable equilibrium position with a constant amplitude and a constant period. It is caused by a restoring force that is proportional to the displacement of the object from its equilibrium position.

2. What is the equation for simple harmonic motion?

The equation for simple harmonic motion is x = A*cos(ωt), where x is the displacement of the object from its equilibrium position, A is the amplitude of the motion, ω is the angular frequency, and t is time.

3. What is the relationship between period and frequency in simple harmonic motion?

In simple harmonic motion, the period (T) and frequency (f) are inversely proportional. This means that as the period increases, the frequency decreases, and vice versa. The relationship can be represented as T = 1/f.

4. What is the difference between simple harmonic motion and uniform circular motion?

Simple harmonic motion involves an object moving back and forth in a straight line, while uniform circular motion involves an object moving in a circular path with a constant speed. However, both types of motion can be described using the same equations and have a periodic nature.

5. What are some real-life examples of simple harmonic motion?

Some common examples of simple harmonic motion include the motion of a pendulum, a mass-spring system, and a tuning fork. Other examples include the motion of a child on a swing, a vibrating guitar string, and the motion of a car's suspension system.

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