Simple harmonic motion and particle speed

[ahhgidaa]

Motion of particle shows a max acc. of 30 m/s2 and a frequency of 120 cycles per minuet. assuming SHM determine, the amplitude and max velocity.

i found the sqrt of k/m to be 12.57 even though neither was given and the frequency to 2 cycles/sec.

i do not know what relations to use to work out the the rst.

Vmax = Xmax sqrt k/m , but where do i get X max

and where do i find Vo

thank you.just trying to figure it out for studying. apparently i suck at it.

 

[WatermelonPig]

Consider that v = dx/dt and a = dv/dt for a point bouncing up and down on the string.

 

[Doc Al]

i found the sqrt of k/m to be 12.57 even though neither was given and the frequency to 2 cycles/sec.

To get ω, just convert the given frequency to radians/sec. (Which you already did.)

Vmax = Xmax sqrt k/m , but where do i get X max

That equation is not quite right. (Look it up again.)

Start with a corresponding equation for the maximum acceleration, which will allow you to solve for the amplitude.

 

[ahhgidaa]

v=dx/dt= -wAsin(wt) and x= Acos(wt)

what is the little t, time. is the time the period? and is 2 cycles per second 2 rad/sec. ?

and just fmi, with the differential equation with x(t) when would i use that. when i have as specific time. I am just unsure about a lot of stuff. sry.

 

[Doc Al]

v=dx/dt= -wAsin(wt)


and x= Acos(wt)

Good. Now you're getting somewhere. Continue to get an equation for the acceleration.

what is the little t, time. is the time the period?

t is just the time, not the period.

and is 2 cycles per second 2 rad/sec. ?

No. To convert from cycles to radians, realize that 1 cycle = 2pi radians.

and just fmi, with the differential equation with x(t) when would i use that. when i have as I am just unsure about a lot of stuff.

Those expressions give you the position and velocity (and, when you get the third equation, acceleration) as a function of time. How would you modify them to get the maximum values of those quantities?

 

[ahhgidaa]

well i found the equations on the next page of my book. ha. and have been looking at them and i do not see how they mathematically went from -wAsin(wt) to just wA for Vmax. I am looking at the graphs to but my math isn't strong enough to see how they could drop the trig func. but the A i got was .189m and and Vmax of 2.35 m/s. and I am glad that I am not afraid to ask questions here because i never do in class which is my bad. but why isn't it s^2.

 

[Doc Al]

well i found the equations on the next page of my book. ha. and have been looking at them and i do not see how they mathematically went from -wAsin(wt) to just wA for Vmax. I am looking at the graphs to but my math isn't strong enough to see how they could drop the trig func.

What's the maximum value of sine or cosine?

but the A i got was .189m and and Vmax of 2.35 m/s.

Close enough.

but why isn't it s^2.

What do you mean? Why isn't what s^2?

 

[ahhgidaa]

for velocity graph the max amplitude is Vmax at 3/4T and for the displacement x at 0 was 3/4T.
how do you get that acc equation? i thinks that's what you were trying to have me do. but what do i think or do to go from V = -wAsin(wt) to Vmax = wA.

dx/dt at x=0? then diff that. which i dnt think i can do.

 

[Doc Al]

for velocity graph the max amplitude is Vmax at 3/4T and for the displacement x at 0 was 3/4T.

Again I ask: What's the maximum value that a sine or cosine function can have?

how do you get that acc equation? i thinks that's what you were trying to have me do.

To get the acceleration equation, use a = dv/dt. Take the derivative of the expression you have for V.

but what do i think or do to go from V = -wAsin(wt) to Vmax = wA.

Note that the only variable is in the sin(wt) part. That's why I'm asking you to tell me what's the maximum value for sin(wt).

 

[ahhgidaa]

1, -1

 

[Doc Al]

1, -1

Right!

So to get the maximum value in those SHM expressions we can replace cos(ωt) and sin(ωt) by 1. (We just care about the magnitude, so sign isn't important.)

So if y = A cos(ωt), then y_max = A. (And so on.)