The velocity of a simple harmonic oscillator is given by;
v = + 6.92*sin(10.5*t) (mks units)
What is its angular frequency?
omega =
What is the amplitude of the motion?
A =
Where is the mass at the time t = 86.08 seconds?
x =
If the mass is 0.53 kg, what is the spring's potential energy?
PE =
What is the kinetic energy?
KE =
To find the angular frequency, amplitude, position at a specific time, potential energy, and kinetic energy of the simple harmonic oscillator, we'll need to use the given equation.
1. Angular Frequency (ω):
The general equation for a simple harmonic oscillator is given by v = A*sin(ωt), where v is the velocity, A is the amplitude, ω is the angular frequency, and t is the time.
Comparing the given equation with the general equation, we find that the angular frequency is 10.5 rad/s. So, ω = 10.5 rad/s.
2. Amplitude (A):
From the given equation, we can see that the amplitude is the coefficient of the sine function, which is 6.92. Therefore, the amplitude is A = 6.92.
3. Position at a specific time (x):
To find the position at a specific time, we need to integrate the velocity equation. The equation for position (x) as a function of time (t) is x = -A*cos(ωt) + x₀, where x₀ is the initial position.
Since we don't have the initial position, we can't find the exact position. However, we can find the displacement from the equilibrium position at a specific time. To do this, substitute the given time (t = 86.08 s) into the equation and calculate the value of x.
4. Potential Energy (PE):
The potential energy (PE) of a simple harmonic oscillator is given by PE = 0.5*k*x², where k is the spring constant and x is the displacement from the equilibrium position.
The spring constant (k) can be found using the equation k = m*ω², where m is the mass of the oscillator.
From the given equation, we know the angular frequency (ω = 10.5 rad/s) and the mass (m = 0.53 kg). Substitute these values into the equation to find the spring constant (k). Then, substitute the displacement (x) into the potential energy (PE) equation to find the potential energy.
5. Kinetic Energy (KE):
The kinetic energy (KE) of a simple harmonic oscillator is given by KE = 0.5*m*v², where m is the mass of the oscillator and v is the velocity.
From the given equation, we know the mass (m = 0.53 kg) and the velocity equation. Substitute these values into the kinetic energy (KE) equation to find the kinetic energy.
By following these steps, you can find the values of the angular frequency (ω), amplitude (A), position at a specific time (x), potential energy (PE), and kinetic energy (KE) for the given simple harmonic oscillator.