# second order differential equations (spring)

Printable View

• Nov 11th 2009, 04:47 PM
yen yen
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
• Nov 11th 2009, 06:51 PM
Coomast
Quote:

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
• Nov 11th 2009, 06:53 PM
yen yen
Quote:

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
• Nov 12th 2009, 12:07 PM
Coomast
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