A 4.40kg block hangs from a spring with spring constant 2160N/m . The block is pulled down 4.60cm from the equilibrium position and given an initial velocity of 1.40m/s back toward equilibrium.
What is the frequency of motion?
What is the amplitude?
What is the total mechanical energy of motion?
To find the frequency of motion, amplitude, and total mechanical energy of the motion, we need to use the equations of motion for a mass-spring system.
1. Frequency of motion:
The frequency of motion can be found using the equation:
f = (1/2π) * √(k/m)
Where,
f is the frequency of motion,
k is the spring constant,
m is the mass of the block.
Plugging in the given values:
k = 2160 N/m
m = 4.40 kg
f = (1/2π) * √(2160 / 4.40)
Evaluating this expression will give us the frequency of motion.
2. Amplitude:
The amplitude of motion is the maximum displacement of the block from its equilibrium position. In this case, it is given as 4.60 cm.
3. Total mechanical energy of motion:
The total mechanical energy of motion is the sum of the potential energy (E_p) and kinetic energy (E_k).
The potential energy of the mass-spring system is given by:
E_p = (1/2) * k * (x^2)
Where,
k is the spring constant,
x is the displacement of the block from the equilibrium position.
The kinetic energy of the block is given by:
E_k = (1/2) * m * v^2
Where,
m is the mass of the block,
v is the velocity of the block.
To find the total mechanical energy (E_total), we need to find both E_p and E_k and sum them up:
E_total = E_p + E_k
Plugging in the given values:
k = 2160 N/m
x = 4.60 cm
m = 4.40 kg
v = 1.40 m/s
Solving these equations will give us the total mechanical energy of motion.
By following these steps, you can find the frequency of motion, amplitude, and total mechanical energy of the given mass-spring system.