Simple Harmonic Motion of a body

In summary, Simple Harmonic Motion (SHM) is a type of periodic motion where a body moves back and forth around a central equilibrium position due to the restoring force of a spring or pendulum. It has a constant period and amplitude and is affected by factors such as mass, force constant, and amplitude. The equation for SHM is x(t) = A*cos(ωt + φ), and it differs from other types of periodic motion in its specific sinusoidal pattern. Additionally, SHM involves the conversion of potential energy into kinetic energy, maintaining a constant total energy.
  • #1
v_pino
169
0

Homework Statement



A body is in simple harmonic motion of amplitude 0.50m and period 4pie seconds. What is the speed of the body when the displacement of the body is 0.30 m?



Homework Equations



Would it be x=Acos2(pie)ft ?

The Attempt at a Solution



I tried substituing in x= 0.30 and A=0.50 and f= (1/ 4pie)

The answer should be 0.20 ms^-1
 
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  • #2
if the equation you gave was for displacement, then you will need to differentiate it to find the function of velocity.
 
  • #3
.

I can confirm that the formula you have used is correct for simple harmonic motion. However, there is a small error in your calculation. The value of f should be 1/4pi, not 1/4pie. Therefore, the correct value for the speed would be 0.20 ms^-1. It is important to pay attention to units and use the correct values in equations to ensure accurate results.
 

Related to Simple Harmonic Motion of a body

What is Simple Harmonic Motion?

Simple Harmonic Motion (SHM) is a type of periodic motion where a body moves back and forth around a central equilibrium position due to the restoring force of a spring or pendulum. It follows a sinusoidal pattern and has a constant period and amplitude.

What are the factors that affect Simple Harmonic Motion?

The factors that affect Simple Harmonic Motion include the mass of the object, the force constant of the spring, and the amplitude of the motion. The frequency of the motion is also affected by these factors.

What is the equation for Simple Harmonic Motion?

The equation for Simple Harmonic Motion is x(t) = A*cos(ωt + φ), where x is the displacement of the body, A is the amplitude of the motion, ω is the angular frequency, and φ is the phase constant.

What is the difference between Simple Harmonic Motion and Periodic Motion?

Simple Harmonic Motion is a type of periodic motion that follows a specific sinusoidal pattern and has a constant period and amplitude. However, periodic motion can take on various forms and does not necessarily follow a sinusoidal pattern.

How is Simple Harmonic Motion related to energy?

Simple Harmonic Motion involves the conversion of potential energy into kinetic energy and vice versa as the body moves back and forth. The total energy of a system in SHM remains constant, as energy is transferred between potential and kinetic forms.

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