Multiple Choice
A horizontal spring-mass system oscillates with a frequency of 0.40 Hz. What is the spring constant if the mass is 0.5 kg?
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17. Periodic Motion
Intro to Simple Harmonic Motion (Horizontal Springs)
Multiple Choice
In the context of simple harmonic motion of a horizontal spring, at which point is the acceleration of the mass the greatest?
A
At the maximum displacement from equilibrium
B
At the equilibrium position
C
At one-quarter of the maximum displacement
D
At half the maximum displacement
Verified step by step guidance1
Understand that in simple harmonic motion (SHM), the acceleration of the mass is directly related to the displacement from the equilibrium position. This is described by Hooke's Law, which states that the force (and thus acceleration) is proportional to the displacement.
Recall the formula for acceleration in SHM: \( a = -\frac{k}{m}x \), where \( a \) is the acceleration, \( k \) is the spring constant, \( m \) is the mass, and \( x \) is the displacement from the equilibrium position.
Note that the negative sign indicates that the acceleration is always directed towards the equilibrium position, opposing the displacement.
Recognize that the magnitude of acceleration is greatest when the displacement \( |x| \) is greatest, because acceleration is proportional to displacement.
Conclude that the acceleration is greatest at the maximum displacement from equilibrium, as this is when \( |x| \) is at its maximum value.
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