You wish to make a mass on a spring oscillate with a period of 1.00 seconds, to count heartbeats. The spring constant is 50.0 N/m. What mass should you put on the end of the spring?
To determine the mass needed to achieve a desired period of oscillation, we can use the formula for the period of a mass-spring system:
T = 2π√(m/k)
Where:
T = period (in seconds)
m = mass (in kilograms)
k = spring constant (in Newtons per meter)
In your case, you want a period (T) of 1.00 seconds and the spring constant (k) is given as 50.0 N/m.
Rearranging the formula to solve for mass (m):
m = (T^2 * k) / (4π^2)
Plugging in the given values:
m = (1.00^2 * 50.0) / (4 * π^2)
Now, let's calculate the mass needed.