Simple Harmonic Motion Query

Hi, in a simple harmonic motion, is the acceleration in the same direction as the displacement and velocity? is the force in the same direction as the velocity? is the velocity in the same direction as the displacement? Thanks :smile:

Reply 1

Fox Corner

21

Hiya - what subject is this for? I'll move it into the specific subject forum and you'll be more likely to get a good answer there :h:

Reply 2

pineneedles

14

Original post by Charlie1523

Hi, in a simple harmonic motion, is the acceleration in the same direction as the displacement and velocity? is the force in the same direction as the velocity? is the velocity in the same direction as the displacement? Thanks :smile:

Acceleration is in the opposite direction to displacement: imagine a mass on a string: as the mass swings to the side, its displacement increases away from the equilibrium position whilst it accelerates towards the equilibrium position.
Force is proportional to acceleration so the above is true for force also.
Velocity is in the same direction as displacement.

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Reply 3

pineneedles

14

Original post by Fox Corner

Hiya - what subject is this for? I'll move it into the specific subject forum and you'll be more likely to get a good answer there :h:

This is supposed to be physics 😃

Posted from TSR Mobile

Reply 4

aamirac

20

Original post by Charlie1523

Hi, in a simple harmonic motion, is the acceleration in the same direction as the displacement and velocity? is the force in the same direction as the velocity? is the velocity in the same direction as the displacement? Thanks

Think of it as a mass on a string, if the spring applies no force that means both the displacement and acceleration would be zero.

In the case where the displacement and acceleration are at it's maximum due to the string applying it's maximum force. The force (acceleration) on the string would then be in the opposite direction to the displacement.
Hence why the equation is

a=-\omega ^2x

Original post by Fox Corner

Hiya - what subject is this for? I'll move it into the specific subject forum and you'll be more likely to get a good answer there :h:

This is Physics btw, thank you. :colondollar:

Reply 5

Asuna Yuuki

9

It's best to remember it using its derivations, i.e. if:

x = asin(ωt)

v = dx/dt = ωacos(ωt)

a = F/m = dv/dt = -ω²asin(ωt)

... comparing the functions, acceleration and force are in the opposite direction to the displacement, and the velocity is in antiphase with the others.

:cute:

Reply 6

Ollie231213

7

Original post by Charlie1523

Hi, in a simple harmonic motion, is the acceleration in the same direction as the displacement and velocity? is the force in the same direction as the velocity? is the velocity in the same direction as the displacement? Thanks :smile:

Think of a mass hanging on a spring in its equilibrium position (displacement = 0). What happens if you then pull it down and let go?

The restoring force will act upwards, towards the equilibrium position, and so the acceleration must act in the same direction (F=ma). The mass's velocity must also be upwards.

But what happens once the mass has gone past the equilibrium position? The mass is still travelling upwards but the displacement is now negative (because it's the other side of the equilibrium position), and now the force and acceleration are now acting downwards. The mass's velocity decreases until it stops -at this point it has reached maximum negative displacement. It then starts accelerating downwards, so the velocity also acts downwards.

So, the force and acceleration always act in the opposite direction to displacement, as this is characteristic of simple harmonic motion. However, the relative directions of the velocity and the acceleration and displacement vary.

See the posts above for a mathematical explanation.