The function x = (6.0 m) cos [(3π rad/s)t+π/3 rad] gives the simple harmonic motion of a body. The speed as it passes through the equilibrium position is _____ m/s. Round your answer to the nearest tenth.
Question
The function x = (6.0 m) cos [(3π rad/s)t+π/3 rad] gives the simple harmonic motion of a body. The speed as it passes through the equilibrium position is _____ m/s. Round your answer to the nearest tenth.
Solution
The speed of an object in simple harmonic motion as it passes through the equilibrium position is given by the formula v = ωA, where ω is the angular frequency and A is the amplitude.
From the given function, we can identify the amplitude A as 6.0 m and the angular frequency ω as 3π rad/s.
Substituting these values into the formula gives:
v = ωA = (3π rad/s)(6.0 m) = 18π m/s.
Rounding to the nearest tenth gives approximately 56.5 m/s.
Similar Questions
The function x = (6.0 m) cos [(3π rad/s)t+π/3 rad] gives the simple harmonic motion of a body. The magnitude of the acceleration at an endpoint is _____ m/s². Round to the nearest whole number.
A particle undergoes simple harmonic motion of amplitude x0 and frequency f . What is theaverage speed of the particle during one oscillation?
Assume a body performing harmonic oscillation, with the oscillation period of T = 6 s; the initial phase is zero. Calculate how long (in seconds) after the beginning of the motion the body displacement from equilibrium position will be one half of the amplitude.
A particle executes simple harmonic motion with an amplitude of 4 cm4 cm. At the mean position, the velocity of the particle is 10 cm s−110 cm s-1. The distance of the particle from the mean position when its speed becomes 5 cm s−15 cm s-1 is
The motion of a particle executing simple harmonic motion is given by X= 0.01 sin 100π (t + 0.05), where X is in metres and t in second. The timeperiod in second is
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.