Finding Velocity& Acceleration

[kggirl]

Please help with the following question:

The position of a mass hanging from a spring and oscillating up and down is given by S[t] = 5sin[2 pie/3 t]. Use the chain rule to find the velocity V[t] and the acceleration a[t] and evaluate S[0], V[0] and a[0].

This is what I have so far:

Position: S[t] = 5 sin[2pie/3 t]
Velocity: d/dt = (5sin 2pie/3 t) = 5 cos 2pie/3 t)
Acceleration: d/dt = (5 cos 2pie/3 t) = -5 sin 2pie/3 t

I'm not sure what the next step is [/list][/code]

 

[stapel]

Do you mean "(2pi)/(3t)", or "(2pi/3)t", or something else?

Note: The Greek letter you learned about back in geometry is called "pi"; "pie" is something you eat.

What is the significance of the brackets? (Your functions aren't formatted with the customary parentheses, such as "S(t)", and I don't know what this is meant to indicate.)

To evaluate S[0], if this means the same thing as "S(0)", just plug in "zero" for "t", and simplify.

When taking the derivative, you might want to state what you're taking the derivative of. "d/dt" doesn't really say anything, but "dS/dt" does, and is, I think, what you meant.

Until it is clear what the original function is, I hesitate to comment on the correctness of the rest of the post.

Please reply with clarifications. Thank you.

Eliz.

 

[kggirl]

Do you mean "(2pi)/(3t)", or "(2pi/3)t", or something else?

Note: The Greek letter you learned about back in geometry is called "pi"; "pie" is something you eat.

What is the significance of the brackets? (Your functions aren't formatted with the customary parentheses, such as "S(t)", and I don't know what this is meant to indicate.)

To evaluate S[0], if this means the same thing as "S(0)", just plug in "zero" for "t", and simplify.

When taking the derivative, you might want to state what you're taking the derivative of. "d/dt" doesn't really say anything, but "dS/dt" does, and is, I think, what you meant.

Until it is clear what the original function is, I hesitate to comment on the correctness of the rest of the post.

Please reply with clarifications. Thank you.
Eliz.

it is 5 sin 2pi/3 t that is the way the question was written with the t inside of the bracket

ds/dt = d/dt

 

[stapel]

Yes, I understand that "t" is part of the argument of the sine. But is it in the numerator, as "(2pi/3)t", or in the denominator, as "(2pi)/(3t)"?

Also, "d/dt" cannot always mean "dS/dt" (assuming you mean "S" and "s" to be, contrary to mathematical practice, the same variable), as this would require a(t), the acceleration, to be the same as the velocity, which it isn't.

Eliz.