If the mass of a simple harmonic oscillator is doubled while keeping the spring constant the same, how does the period change?
Correct Answer: Period increases
- Step 1: Understand the formula for the period of a simple harmonic oscillator, which is T = 2π√(m/k).
- Step 2: Identify the variables in the formula: T is the period, m is the mass, and k is the spring constant.
- Step 3: Note that in this scenario, the spring constant k remains the same.
- Step 4: Recognize that if the mass m is doubled, we can represent the new mass as 2m.
- Step 5: Substitute the new mass into the formula: T' = 2π√(2m/k).
- Step 6: Simplify the new period: T' = 2π√(2) * √(m/k) = √(2) * T.
- Step 7: Conclude that since √(2) is greater than 1, the new period T' is greater than the original period T.
- Simple Harmonic Motion – The behavior of oscillating systems, characterized by a restoring force proportional to displacement.
- Period of Oscillation – The time taken for one complete cycle of motion in a harmonic oscillator, dependent on mass and spring constant.
- Effect of Mass on Period – In a simple harmonic oscillator, the period increases with an increase in mass when the spring constant remains constant.
