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 the mass that should be attached for the spring to oscillate with a period of 1.85s, we need to understand the relationship between the period of oscillation and the mass attached to the spring.
The period of oscillation (T) for a mass-spring system can be calculated using the formula:
T = 2π √(m/k)
where:
T is the period of oscillation,
m is the mass attached to the spring, and
k is the spring constant.
In this case, we have the initial mass (m1 = 1.55kg) and its corresponding period (T1 = 1.52s). We want to find the mass (m2) that results in a new period (T2 = 1.85s).
We can rearrange the formula to solve for the unknown mass:
m2 = (T2^2 / T1^2) * m1
Now let's substitute the known values and solve for m2:
m2 = (1.85s^2 / 1.52s^2) * 1.55kg
Calculating this expression, we have:
m2 = (3.4224 / 2.3104) * 1.55kg
m2 ≈ 2.032kg
Therefore, a mass of approximately 2.032kg should be attached to the spring for it to oscillate with a period of 1.85s.