An object in simple harmonic motion has an amplitude of 0.202 m and an oscillation period of 0.620 s. Determine the maximum speed of the motion.
T = 2pi*SQRT(L/g) solve for length L of the pendulum
Then, solve for the max angle, knowing L and amplitude
sin theta=Amplitude/L
then compute theta.
Finally, vmax= √{2gL[1-cos(Theta)]}
v(max) =Aω= 2πA/T
To determine the maximum speed of an object in simple harmonic motion, you need to know the amplitude and period of the motion. The formula to calculate the maximum speed is v_max = Aω, where v_max is the maximum speed, A is the amplitude, and ω is the angular frequency.
First, let's find the angular frequency (ω). The formula to calculate the angular frequency is ω = 2π/T, where T is the period of the motion.
Using the given period T = 0.620 s, we can calculate the angular frequency:
ω = 2π / T = 2π / 0.620 = 10.159 rad/s (rounded to three decimal places).
Now we can substitute the value of ω into the formula for the maximum speed:
v_max = Aω = 0.202 × 10.159 = 2.052 m/s (rounded to three decimal places).
Therefore, the maximum speed of the motion is approximately 2.052 m/s.