Final answer:
To determine the mass needed for the spring to oscillate with a period of 1.0 s, we can use the formula for the period of an oscillating mass-spring system. By plugging in the given values, we can solve for the mass.
Step-by-step explanation:
To find the mass that must be suspended from the spring to achieve a period of 1.0 s, we can use the formula for the period of an oscillating mass-spring system:
Calculating the Required Mass for a Specific Oscillation Period
To calculate the mass that must be suspended from a spring to achieve a certain period of oscillation, we use the formula for the period (T) of a simple harmonic oscillator, T=2π√(m/k), where 'm' is the mass and 'k' is the spring constant. Given a spring constant (k) of 40.0 N/m and a desired period (T) of 1.0 s, we rearrange the formula to solve for mass (m): m = √((T/2π)² ∙ k). Inserting the values, we get m = √((1.0/2π)² ∙ 40.0 N/m), which simplifies to m = 0.159 kg or 159 g.
Period = 2π√(m/k)
Given that the force constant (k) of the spring is 40.0 N/m and the desired period is 1.0 s, we can rearrange the formula to solve for the mass (m):
m = (Period^2 * k) / (4π^2)
Substituting the given values, we get: m = (1.0^2 * 40.0) / (4π^2)
Simplifying the expression gives us the mass required for the system to oscillate with a period of 1.0 s.