A system exhibits simple harmonic motion with a frequency of 0.85 cycles per second. Calculate the acceleration experienced by the mass 3.0 m from the equilibrium point.
To calculate the acceleration experienced by the mass, we can use the formula for acceleration in simple harmonic motion:
a = -ω^2 * x
Where:
a is the acceleration,
ω is the angular frequency, and
x is the displacement from the equilibrium point.
First, we need to find the angular frequency (ω). The frequency (f) is given as 0.85 cycles per second. The angular frequency is related to the frequency by the equation:
ω = 2πf
Substituting the given frequency into the equation:
ω = 2π * 0.85
Next, we need to calculate the displacement (x). The mass is given to be 3.0 m from the equilibrium point.
Finally, we can substitute the values of ω and x back into the acceleration formula to find the answer.
To calculate the acceleration experienced by the mass, we need to use the formula for the acceleration in simple harmonic motion:
a = -ω^2 x
where a is the acceleration, ω is the angular frequency, and x is the displacement of the mass from the equilibrium position.
First, let's calculate the angular frequency (ω). The angular frequency is related to the frequency (f) by the equation:
ω = 2πf
Given that the frequency is 0.85 cycles per second, we can calculate the angular frequency as follows:
ω = 2π × 0.85 ≈ 5.36 rad/s
Next, we need to calculate the displacement (x) of the mass from the equilibrium position. It is given that the mass is 3.0 m from the equilibrium point.
Now, we can substitute the values of angular frequency (ω) and displacement (x) into the formula for acceleration (a):
a = -ω^2 x
a = -(5.36 rad/s)^2 × 3.0 m
Calculating this expression will give us the acceleration experienced by the mass.
you know that sin(kt) has period 2π/k, so its frequency is k/2π
So, you need to find k such that k/2π = 0.85
Then just take the 2nd derivative of that to find the acceleration.
the 2nd derivative of sin(kx) is just -k^2 sin(kx)