Solving Simple Harmonic Motion Question

In summary, the conversation discusses the use of general SHM equations and whether they can still be applied when a particle is given a velocity towards the center of SHM while maintaining the same force. The question also arises whether this should be considered a new SHM or if the equations should be derived again. The complexity of deriving the equation of motion for this scenario is also mentioned.
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acmmanoj
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I am having a question and tries to solve a problem for days. Consider general SHM. When the particle reaches to the maximum displacement, a if a velocity U is given to the particle towards to the center of SHM, (keeping the same force mω^2x)

1. What would happen to the SHM...is it same or can i use same equations or should i derive equation again

Should i consider this as new SHM ( X=a when t=0) or should i continue from same SHM (X=0 when T=0)

2. if i derive again, which point should i considered as center, what will happen to the displacement and maximum displacement...is it same or difference

3. when tries to get equation of motion as x=asin(ωt) from intergartion it produces a very complex equation. (in intergration i took, when x=a , v=u and x=a t=0)
 
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FAQ: Solving Simple Harmonic Motion Question

What is simple harmonic motion?

Simple harmonic motion is a type of periodic motion where an object moves back and forth in a straight line, with a constant amplitude and a sinusoidal pattern. This type of motion is caused by a restoring force that is proportional to the displacement from the equilibrium position.

How do you calculate the period of simple harmonic motion?

The period of simple harmonic motion can be calculated by dividing the time taken for one complete cycle by the number of cycles. Mathematically, it can be represented as T = 2π√(m/k), where T is the period, m is the mass of the object, and k is the spring constant.

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

The frequency of simple harmonic motion is the number of cycles per unit time, and it is inversely proportional to the period. This means that as the frequency increases, the period decreases, and vice versa. Mathematically, it can be represented as f = 1/T.

4. How does amplitude affect simple harmonic motion?

The amplitude of simple harmonic motion is the maximum displacement of the object from its equilibrium position. It does not affect the period or frequency of the motion, but it does affect the maximum velocity and acceleration of the object. The larger the amplitude, the greater the velocity and acceleration.

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 on a spring, and the back and forth motion of a diving board. Other examples include the motion of a swing, a vibrating guitar string, and the rotation of a ceiling fan.

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