When a 1.55kg mass is attached to a spring it oscillates with a period of 1.52s.
What mass should be attached for it oscillate with a period of 1.85s.
To determine what mass should be attached to the spring for it to oscillate with a period of 1.85s, we can use the relationship between the period (T) and the mass (m) for a mass-spring system.
The period of oscillation (T) for a mass-spring system is given by the following formula:
T = 2π√(m/k)
Where:
- T is the period of oscillation (in seconds)
- m is the mass attached to the spring (in kilograms)
- k is the spring constant (in Newtons per meter)
We are given that when a 1.55kg mass is attached to the spring, it oscillates with a period of 1.52s. Let's denote this situation as m1 and T1:
m1 = 1.55kg
T1 = 1.52s
Using these values, we can rearrange the formula to solve for the spring constant (k):
k = (4π²m1) / T1²
Now that we know the spring constant (k) for this system, we can use it to find the mass (m2) that should be attached to the spring for a desired period (T2).
T2 = 1.85s
Rearranging the formula again, we can solve for the mass (m2):
m2 = (T2²k) / (4π²)
Now let's substitute the given values and calculate the mass (m2):
m2 = (1.85s² * k) / (4π²)
To calculate the mass (m2), we first need to determine the spring constant (k) using the mass (m1) and period (T1) values given:
k = (4π² * 1.55kg) / (1.52s²)
Now, substitute this value of k into the formula for m2:
m2 = (1.85s² * [(4π² * 1.55kg) / (1.52s²)]) / (4π²)
By simplifying and canceling out common terms, we find:
m2 ≈ 2.05kg
Therefore, a mass of approximately 2.05kg should be attached for the spring to oscillate with a period of 1.85s.