Quick Question: Frequency & Period for SHM

[ilovemcat]

TPR Gives two different equations to find the Frequency and Period for an object under-going SHM (Simple Harmonic Motion):

For a spring, the equations they give are:

F = 1/2pi x sqrt (k/m)
T = 2pi x sqrt (m/k) - where k is spring constant and m is mass

For a pendulum (assuming small angle is proportional to displacement):

F = 1/2pi x sqrt (g/l)
T = 2pi x sqrt (l/g) - where g is acceleration due to gravity and l is length of pendulum

Then, EK gives this equation to find angular frequencies for a spring and pendulum:

w (omega) = sqrt (k/m) <-- Spring
w (omega) = sqrt (g/l) <-- Pendulum

I'm just curious, how important do you think it is to remember these equations. Would they be provided in a passage? I probably wouldn't remember them come MCAT time. I have bad memory recall.

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[ilovemcat]

And one more question, regarding the the equations for a Pendulum... I really didn't understand the explanation TPR tried to give regarding the proportionality of the restoring force with displacement, but is it fair to assume that for most MCAT related problems of this type, that for a pendulum restoring force is proportional to displacement? They mention that this is only the case when the angle is really small, but I have no idea how "small" an angle needs to be for this equation to be valid.

 

[PiBond]

TPR Gives two different equations to find the Frequency and Period for an object under-going SHM (Simple Harmonic Motion):

For a spring, the equations they give are:

F = 1/2pi x sqrt (k/m)
T = 2pi x sqrt (m/k) - where k is spring constant and m is mass

For a pendulum (assuming small angle is proportional to displacement):

F = 1/2pi x sqrt (g/l)
T = 2pi x sqrt (l/g) - where g is acceleration due to gravity and l is length of pendulum

Then, EK gives this equation to find angular frequencies for a spring and pendulum:

w (omega) = sqrt (k/m) <-- Spring
w (omega) = sqrt (g/l) <-- Pendulum

I'm just curious, how important do you think it is to remember these equations. Would they be provided in a passage? I probably wouldn't remember them come MCAT time. I have bad memory recall.

I personally learned the TPR equations, didn't know the EK ones. I think they're extremely important in the event you get a question asking about the effects on period/frequency if a certain variable is altered. If you're having trouble learning them, here's a good pneumonic for Period of a spring: it's time (period) to eat 2 pi with a squirt (square root) of milk (m/k). Of course, the frequency is just the inverse of the period.

You could venture to supply the same pneumonic for the period of a pendulum: time to eat 2pi with a squirt of leg. It just sounds weird so it sticks for me.

 

[PiBond]

And one more question, regarding the the equations for a Pendulum... I really didn't understand the explanation TPR tried to give regarding the proportionality of the restoring force with displacement, but is it fair to assume that for most MCAT related problems of this type, that for a pendulum restoring force is proportional to displacement? They mention that this is only the case when the angle is really small, but I have no idea how "small" an angle needs to be for this equation to be valid.

if i remember correctly, the restoring force is just mgsin(theta). however, when we displace a pendulum at a large angle (I think I remember learning more than 15 degrees) our pendulum fails to undergo SHM for several reasons.

 

[ilovemcat]

I personally learned the TPR equations, didn't know the EK ones. I think they're extremely important in the event you get a question asking about the effects on period/frequency if a certain variable is altered. If you're having trouble learning them, here's a good pneumonic for Period of a spring: it's time (period) to eat 2 pi with a squirt (square root) of milk (m/k). Of course, the frequency is just the inverse of the period.

You could venture to supply the same pneumonic for the period of a pendulum: time to eat 2pi with a squirt of leg. It just sounds weird so it sticks for me.

Interesting mnemonic, haha. I'll stuff that bit of knowledge somewhere in my brain. Thanks for the tip.

 

[ilovemcat]

if i remember correctly, the restoring force is just mgsin(theta). however, when we displace a pendulum at a large angle (I think I remember learning more than 15 degrees) our pendulum fails to undergo SHM for several reasons.

Ah okay. I'll follow that rule then. Thanks again 🙂

 

[Rabolisk]

You really only need to know one of those equations, because the rest can be easily derived from one of them. The relationship between frequency, angular frequency, and period is easy to memorize. What I would memorize is that frequency is directly proportional to the square root of k or g and inversely proportional to the square root of m or l.