A begginners question on S.H.M

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In summary, the conversation discusses the solution of a differential equation for simple harmonic motion, which has two possible representations using either a sine or cosine function. The difference lies in the use of the variable "phi". Both representations are valid and can be used to derive the velocity and acceleration of a particle in SHM.
  • #1
creativeassault
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Hello,
this is my first post on this forum and it is about simple harmonic motion. I can't seem to understand why the displacement x has two functions. What I mean is, x(t)=A.Sin(wt+phi) is the solution of differential equation of s.h.m; which is used by our physics teacher to derive the velocity and acceleration of a particle performing s.h.m; BUT in many textbooks I found that x(t)=A.Cos(wt+phi) ... my question is how can there be two values for x ?

Any help would be very helpfull,
Thank You.
Rohit Arondekar.
 
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  • #2
Both versions are perfectly acceptable, as long as you remember that the "phi" in the sine representation will differ from the "phi" in the cosine representation, since we have, in general:
[tex]\cos(\theta-\frac{\pi}{2})=\sin(\theta)[/tex]
 
  • #3
Yay! cheers arildno :)
 

1. What is Simple Harmonic Motion (S.H.M)?

Simple Harmonic Motion (S.H.M) is a type of periodic motion in which an object oscillates back and forth around a central equilibrium point. This motion is characterized by a restoring force that is directly proportional to the displacement from the equilibrium position.

2. What are the factors that affect the period of S.H.M?

The period, or the time it takes for one complete oscillation, of S.H.M is affected by two main factors: the mass of the object and the stiffness of the spring. A heavier mass or a stiffer spring will result in a longer period, while a lighter mass or a less stiff spring will result in a shorter period.

3. How is the amplitude of S.H.M related to the energy of the system?

The amplitude, or the maximum displacement from the equilibrium position, of S.H.M is directly proportional to the energy of the system. This means that a larger amplitude results in a higher energy, while a smaller amplitude results in a lower energy.

4. Can S.H.M occur in any direction?

Yes, S.H.M can occur in any direction as long as there is a restoring force acting on the object. This means that S.H.M can occur in a linear, circular, elliptical, or any other type of path.

5. How is S.H.M different from other types of motion?

S.H.M is different from other types of motion in that it is periodic, meaning it repeats itself in a regular pattern. It also has a restoring force that is proportional to the displacement, making it a special type of oscillatory motion.

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