# Thread: second order differential equations (spring)

1. ## second order differential equations (spring)

im doing revision for my calculus and under second order differential equations under springs-free vibrations, i saw this formula R=(beta)(y with a dot on top)
can anyone tell me what that y with a dot on top means? there is also one with 2 dots on top. i know that the beta is the damping constant. just need help from someone about the y with dots. thanks

2. Originally Posted by yen yen
im doing revision for my calculus and under second order differential equations under springs-free vibrations, i saw this formula R=(beta)(y with a dot on top)
can anyone tell me what that y with a dot on top means? there is also one with 2 dots on top. i know that the beta is the damping constant. just need help from someone about the y with dots. thanks
Hello yen yen,

The dot means nothing more than the derivative with respect to time of the variable you're looking at, p.e.

$\displaystyle \dot{x}=\frac{dx}{dt}$

double dots mean: take the derivative twice...

hope this helps,

Coomast

3. Originally Posted by Coomast
Hello yen yen,

The dot means nothing more than the derivative with respect to time of the variable you're looking at, p.e.

$\displaystyle \dot{x}=\frac{dx}{dt}$

double dots mean: take the derivative twice...

hope this helps,

Coomast
oh. so y with a dot on top is the same as y'? silly me... should have paid attention in lectures. thanks

4. No, the dot means to take the derivative with respect to time, an accent means with respect to another variable, p.e. x (it can also mean time t though). They both mean indeed the derivative but the dot is used more in mechanics (time), while the accent is used more in mathematics (any variable, p.e. x or t). Is this clearing the difference?

It can be confusing, and to be honest I do not know why they use a different symbol for the time derivative in mechanics. In math this difference is not made, at least as far as I know.

Coomast