# When a mass is in SHM, what is the relationship between velocity and acceleration?

## Main Question or Discussion Point

When a mass is in SHM, and is moving towards equilibrium point, its velocity starts to increase but why does acceleration decreases? What is the gradient when velocity is increasing and when it is at maximum? Thanks a lot!!

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berkeman
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Can you find a plot of the position, velocity and acceleration of a mass in SHM and provide a link? Are you familiar with the equation for the position of the mass versus time, and how to differentiate it to get the velocity and acceleration?

I am only familiar with the displacement,velocity, and acceleration time graphs but I don't understand them quite well. The diagram attached shows the simple pendulum I am referring to

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Yea, I am familiar with these sinusoidal graphs but i still don't know why acceleration decreases while velocity increases although I understand as to why acceleration increases as velocity decreases due to the increase in the retarding force

Yea, I am familiar with these sinusoidal graphs but i still don't know why acceleration decreases while velocity increases although I understand as to why acceleration increases as velocity decreases due to the increase in the retarding force
Furthermore, I also struggle in trying to understand the equation of x=asin(wt) but this can be because i dont study maths at advanced level

The velocity (actually the speed or the magnitude of velocity) decreases when the acceleration is negative. Nothing to do with the fact that the acceleration is increasing or decreasing. It could be constant negative acceleration and the velocity will decrease too.

The relation between velocity and acceleration is the same for any system: velocity is the first derivative of acceleration in respect to time. Positive acceleartion means that the velocity increases and negative acceleration means that velocity decreases.

When a mass is in SHM, and is moving towards equilibrium point, its velocity starts to increase but why does acceleration decreases? What is the gradient when velocity is increasing and when it is at maximum? Thanks a lot!!
In SHM when a mass moves towards equilibrium position, by definition it is restoring itself to a neutral position. Hence, at equilibrium position the force acting on it would be zero (since if it still had force acting on it, it would not be called a neutral or equilibrium position). But while coming back to the neutral position it gains a lot of momentum or velocity on account of force that is continuously accelerating it and therefore increasing the velocity till it maxes at equilibrium position since at this point the force acting is zero. And on account of Newton's 1st law of motion, it continues to swing to the other end.

jtbell
Mentor
i still don't know why acceleration decreases while velocity increases
Do you know any calculus, specifically differential calculus and the derivatives of sine and cosine functions?