Equation of shm for different positions

In summary, the homework assignment asks for the equation of a particle in simple harmonic motion with amplitude a and angular frequency w, taking into account all distances from one extreme position and time when the particle is at the opposite extreme end. The resulting equation should measure distances from an origin at one extreme position and time from a clock that starts at zero when the particle is at the opposite extreme position from the origin. The equation for this would be X = A sin (wt + ∆) with a phase difference of ∆ representing the initial position of the particle.
  • #1
Shivang kohlii
19
1

Homework Statement


Write the equation for a particle in simple harmonic motion with amplitude a and angular frequency w considering all distances from one extreme position and time when it is at other extreme end.

Homework Equations



X = A sin (wt + ∆)
∆ = phase difference

The Attempt at a Solution


I couldn't fully understand the question and what we should do to obtain the answer...
Any insight to the question and the steps related to it would be very much appreciated!
 
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  • #2
Shivang kohlii said:

Homework Statement


Write the equation for a particle in simple harmonic motion with amplitude a and angular frequency w considering all distances from one extreme position and time when it is at other extreme end.

Homework Equations



X = A sin (wt + ∆)
∆ = phase difference

The Attempt at a Solution


I couldn't fully understand the question and what we should do to obtain the answer...
Any insight to the question and the steps related to it would be very much appreciated!
You have written the most general expression for the position of the harmonic oscillator. You are asked to write an expression such that distances are measured from an origin at one of the extreme positions and time is measured by a clock that shows zero time when the particle is at the opposite extreme position from the origin.
 

1. What is the equation for simple harmonic motion (SHM) at different positions?

The equation for SHM at different positions is x = A cos(ωt + φ), where x is the displacement from equilibrium, A is the amplitude of the motion, ω is the angular frequency, and φ is the phase constant.

2. How does the amplitude affect the equation of SHM for different positions?

The amplitude, A, represents the maximum displacement from equilibrium. It affects the equation of SHM by determining the maximum displacement at different positions. As A increases, the maximum displacement also increases, resulting in a larger range of motion.

3. How does the angular frequency affect the equation of SHM for different positions?

The angular frequency, ω, determines the speed at which the object oscillates. It affects the equation of SHM by determining the rate at which the object moves through different positions. A higher angular frequency results in a faster oscillation and a lower angular frequency results in a slower oscillation.

4. What is the phase constant in the equation of SHM for different positions?

The phase constant, φ, represents the initial phase of the motion. It affects the equation of SHM by determining the starting position of the object at t = 0. A phase constant of 0 means the object starts at its equilibrium position, while a phase constant of π/2 means the object starts at its maximum displacement in the positive direction.

5. Can the equation of SHM for different positions be used for any type of motion?

No, the equation of SHM is only applicable for a specific type of motion where the restoring force is proportional to the displacement from equilibrium. This type of motion is known as simple harmonic motion and can be observed in systems such as a mass-spring system or a pendulum.

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