A spring has an unstretched length of 20 cm. A 100 g mass hanging from the spring stretches it to an equilateral length of 30 cm. suppose the mass is pulled down to where the spring's length is 40 cm. When it is released, it begins to oscillate. What is the amplitude of the oscillation?
To find the amplitude of the oscillation, we need to determine the maximum displacement of the mass from its equilibrium position. In this case, the equilibrium position is when the spring is unstretched, or at its original length of 20 cm.
To find the amplitude, we can calculate the maximum displacement as the difference between the maximum elongation and the original length of the spring.
Step 1: Calculate the elongation when the mass hangs at a length of 30 cm.
The elongation is the difference between the extended length and the original length of the spring.
Elongation = Extended length - Original length
Elongation = 30 cm - 20 cm
Elongation = 10 cm
Step 2: Calculate the elongation when the spring's length is 40 cm.
Elongation = Extended length - Original length
Elongation = 40 cm - 20 cm
Elongation = 20 cm
Step 3: Calculate the amplitude.
Amplitude = Maximum elongation - Original length
Amplitude = 20 cm - 20 cm
Amplitude = 0 cm
Therefore, the amplitude of the oscillation is 0 cm, which means the mass will not oscillate and remain at the equilibrium position.
To find the amplitude of the oscillation, we can start by calculating the maximum elongation of the spring.
Given:
Unstretched length of the spring (L0) = 20 cm
Equilateral length (maximum at rest) (Lmax) = 30 cm
Length when pulled down (Lpull) = 40 cm
To find the maximum elongation (A) of the spring, we can subtract the unstretched length from the equilateral length:
A = Lmax - L0
A = 30 cm - 20 cm
A = 10 cm
Therefore, the amplitude of the oscillation is 10 cm.