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The following notation is used in SHM.

x - Displacement

a - Acceleration

T - Period

w - Angular Frequency

f - Frequency

My question is what does X0 stand for !

And another question for example I am given these equations

x= X0 sin (wt)

x= X0 cos (wt)

How do I know when to use cos or sin? Do I use cos when displacement starts at is max and sin when it starts at zero?

x - Displacement

a - Acceleration

T - Period

w - Angular Frequency

f - Frequency

My question is what does X0 stand for !

And another question for example I am given these equations

x= X0 sin (wt)

x= X0 cos (wt)

How do I know when to use cos or sin? Do I use cos when displacement starts at is max and sin when it starts at zero?

davidsmith

The following notation is used in SHM.

x - Displacement

a - Acceleration

T - Period

w - Angular Frequency

f - Frequency

My question is what does X0 stand for !

And another question for example I am given these equations

x= X0 sin (wt)

x= X0 cos (wt)

x - Displacement

a - Acceleration

T - Period

w - Angular Frequency

f - Frequency

My question is what does X0 stand for !

And another question for example I am given these equations

x= X0 sin (wt)

x= X0 cos (wt)

You know cos and sin functions can go between +/- 1, right? So this means that x can go between +/- x

How do I know when to use cos or sin? Do I use cos when displacement starts at is max and sin when it starts at zero?

Simply put, yes. It depends on what the displacement is when t=0.

This is an example of a choice of phase for your oscillation. You might know that $\cos (\omega t) = \sin (\omega t + \pi/2)$, but even more generally you can write any oscillation as $\sin(\omega t + \phi)$ , where $\phi$ controls where the oscillation is in its cycle at $t=0$ AKA the phase. You can write this explicitly as $\sin(\omega [t + \Delta t])$, where $\Delta t = \phi/\omega$.

Thanks I get it now!

My question is what is this formula finding? is the x for total displacement?

(edited 2 years ago)

Original post by Brooksy1800

My question is what is this formula finding? is the x for total displacement?

In the formula

x= X

x is the displacement of the particle from its equilibrium position at any time t (it's oscillating about that position)

X

When t=0 the sin is zero and the displacement is zero (The particle is at its equilibrium position)

when t is such that the angle wt is 90 degrees, the sin is 1 and x = X

At 180 degs x is zero again, and at 270 degs it's back to maximum.

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