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In the case of sustained force oscillat...

In the case of sustained force oscillations the amplitude of oscillations

A

decreases linearly

B

decreases sinusodially

C

dereases exponentially

D

always remains constant

Text Solution

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The correct Answer is:
To solve the question regarding the amplitude of oscillations in the case of sustained force oscillations, we can follow these steps: ### Step-by-Step Solution: 1. **Understanding the System**: - We have a block attached to a spring with a spring constant \( k \) and mass \( M \). - The system experiences an external periodic force that drives it into oscillation. 2. **Forces Acting on the System**: - The forces acting on the block include: - The spring force, which is given by Hooke's Law as \( F_s = -kx \) (where \( x \) is the displacement from the equilibrium position). - The damping force, which is proportional to the velocity of the block and is given as \( F_d = -bv \) (where \( b \) is the damping coefficient and \( v \) is the velocity). - The external periodic force, which we can denote as \( F_{ext}(t) \). 3. **Net Force on the System**: - The net force acting on the block can be expressed as: \[ F_{net} = F_{ext}(t) + F_d + F_s \] - This net force leads to the motion of the block. 4. **Forced Oscillations**: - In sustained forced oscillations, the external force is applied in such a way that it compensates for the damping force and the spring force, allowing the system to oscillate at a constant amplitude. 5. **Amplitude of Oscillation**: - The amplitude of oscillation in a forced oscillation system is determined by the balance between the driving force and the damping force. - If the external force is constant and periodic, it can maintain a steady amplitude despite the damping effects. 6. **Conclusion**: - In sustained force oscillations, the amplitude of oscillations remains constant over time. Therefore, the correct answer to the question is that the amplitude "always remains constant". ### Final Answer: The amplitude of oscillations in the case of sustained force oscillations always remains constant. ---
To solve the question regarding the amplitude of oscillations in the case of sustained force oscillations, we can follow these steps: ### Step-by-Step Solution: 1. **Understanding the System**: - We have a block attached to a spring with a spring constant \( k \) and mass \( M \). - The system experiences an external periodic force that drives it into oscillation. ...
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