For a child's swing in lightly damped SHM, I am given the time period and a value for g; (as well as the mass.)
with just these, can i rearrange the equation:
T (4s)= 2pi times sqrt l/g
to calculate the length of the swing?
I believe i have (3.98m), but the question says to ignore the mass of the ropes. I'm worried i should use mass, but it seems uneccessary.
Any help appreciated.
Yes, you can rearrange the equation to calculate the length of the swing. In the equation T = 2π√(l/g), T represents the time period, l represents the length of the swing, and g represents the acceleration due to gravity.
To find the length of the swing, you can rearrange the equation as follows:
l = (T^2 * g) / (4π^2)
Given that you have the time period (T) and the value for g, you can substitute these values into the equation and solve for the length (l).
However, in your question, you mention that you were given the mass of the swing. In the equation for the time period of a simple pendulum, the mass does not appear. This is because the time period depends only on the length and the acceleration due to gravity, not the mass.
Therefore, you can safely ignore the mass of the ropes and proceed with calculating the length using the given time period and the value of g. Your calculation of approximately 3.98m is correct.
I hope this clarifies your doubt. If you have any further questions, feel free to ask!