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
Question
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
Solution
In simple harmonic motion, the velocity v of a particle is given by the equation:
v = ω√(A² - x²)
where:
- ω is the angular frequency,
- A is the amplitude, and
- x is the displacement from the mean position.
Given that the amplitude A is 4 cm and the velocity at the mean position (x = 0) is 10 cm/s, we can find ω using the equation:
v = ωA 10 cm/s = ω * 4 cm ω = 10 cm/s / 4 cm = 2.5 s⁻¹
Now, we want to find the displacement x when the velocity v is 5 cm/s. We can use the velocity equation:
5 cm/s = 2.5 s⁻¹ * √(4 cm)² - x² 5 cm/s = 2.5 s⁻¹ * √16 cm² - x² 2 cm/s = √16 cm² - x² 4 cm²/s² = 16 cm² - x² x² = 16 cm² - 4 cm² x² = 12 cm² x = √12 cm = 2√3 cm
So, the distance of the particle from the mean position when its speed becomes 5 cm/s is 2√3 cm.
Similar Questions
A particle executes simple harmonicmotion with an amplitude of 5 cm.When the particle is at 4 cm from themean position, the magnitude of itsvelocity in SI units is equal to that of itsacceleration. Then, its periodic time inseconds is
A particle of mass 0.1 kg0.1 kg is executing simple harmonic motion of amplitude 0.1 m0.1 m. When the particle passes through the mean position, its kinetic energy is 8×10−3 J8×10-3 J. If the initial phase is 45°,45°, the equation of its motion is (Assume, x (t)𝑥 𝑡 as the position of the particle at time t𝑡)
A particle moves rectilinearly with a constant acceleration 1 m/s2. Its speed after 10 seconds is 5 m/s. The distance covered by the particle in this duration is (Initial & final velocities are in opposite direction)
particle of mass 250 g250 g executes a simple harmonic motion under a periodic force F=(–25x) N𝐹=(–25𝑥) N. The particle attains a maximum speed of 4 m s−14 m s-1 during its oscillation. The amplitude of the motion is ______cmcm
A particle in simple harmonic motion while passing through mean position will haveSelect one:a. Minimum kinetic energy and minimum potential energyb. Maximum kinetic energy and maximum potential energyc. Minimum kinetic energy and maximum potential energyd. Maximum kinetic energy and minimum potential energy
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.