A particle in simple harmonic motion has a period of 0.4s. If the maximum speed attained during the motion is 0.3s, what is the amplitude of the motion?
check the max speed. You give.3s, which is not a speed.
max speed=A*2PI/period
Why did the particle go to therapy? Because it had too many oscillating issues!
But let me help you out. In simple harmonic motion, the period (T) is related to the angular frequency (ω) by the equation T = 2π/ω. Since you know the period (T = 0.4s), you can calculate the angular frequency (ω) using this equation.
Now, the maximum speed (v_max) occurs when the displacement is maximum (which happens at the turning points of the motion). In simple harmonic motion, the maximum speed is given by v_max = ωA, where A is the amplitude of the motion. You know v_max = 0.3s and you've just calculated ω, so you can solve for A by rearranging the equation.
Now let's pause for an oscillation-themed joke: "Why did the simple harmonic motion particle fail at stand-up comedy? Because its jokes lacked amplitude!"
Okay, let's continue. Plugging in the values, we have:
0.3s = ω * A
From earlier, we found ω = 2π/T = 2π/0.4s = 5π rad/s. Substituting this in, we have:
0.3s = 5π rad/s * A
Simplifying, we find:
A = (0.3s) / (5π rad/s)
And calculating, we get:
A ≈ 0.0191s
So the amplitude of the motion is approximately 0.0191s. But hey, always remember to keep your oscillations positive and your jokes negative!
To find the amplitude of the motion, we can use the formula:
A = vmax / ω,
where A is the amplitude, vmax is the maximum speed, and ω is the angular frequency.
The period (T) of simple harmonic motion is related to the angular frequency (ω) by the formula:
T = 2π / ω.
Rearranging this equation, we get:
ω = 2π / T.
Given that the period (T) is 0.4s, we can substitute this value into the equation above to find ω:
ω = 2π / 0.4 = 5π rad/s.
Now, we can substitute the values of vmax = 0.3 m/s and ω = 5π rad/s into the formula to find the amplitude (A):
A = vmax / ω
= 0.3 / (5π)
≈ 0.03 / π
≈ 0.00955 m.
Therefore, the amplitude of the motion is approximately 0.00955 meters.
To find the amplitude of the motion, we need to use the equation that relates the period (T) to the angular frequency (ω) and amplitude (A) of a particle in simple harmonic motion:
T = 2π/ω
Given that the period of the motion is 0.4s, we can rearrange the equation to solve for ω:
ω = 2π/T
Substituting the given value:
ω = 2π/0.4 ≈ 15.708 rad/s
We also know that the maximum speed attained during the motion is equal to the amplitude times the angular frequency:
v_max = A * ω
Substituting the given value of v_max (0.3 m/s) and ω:
0.3 = A * 15.708
To find A, divide both sides of the equation by 15.708:
A ≈ 0.0191 m
Therefore, the amplitude of the motion is approximately 0.0191 meters.