Textbook Question
Determine the phase constant ϕ in Eq. 14–4 if, at t = 0, the oscillating mass is at 𝓍 = ― 1/2 A.
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17. Periodic Motion
Intro to Simple Harmonic Motion (Horizontal Springs)
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Join thousands of students who trust us to help them ace their exams!Watch the first videoMultiple 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?
A
0.32 N/m
B
5.00 N/m
C
1.26 N/m
D
3.16 N/m
Verified step by step guidance1
Start by recalling the formula for the frequency of a spring-mass system: \( f = \frac{1}{2\pi} \sqrt{\frac{k}{m}} \), where \( f \) is the frequency, \( k \) is the spring constant, and \( m \) is the mass.
Rearrange the formula to solve for the spring constant \( k \): \( k = (2\pi f)^2 m \).
Substitute the given values into the equation: \( f = 0.40 \text{ Hz} \) and \( m = 0.5 \text{ kg} \).
Calculate \( (2\pi f)^2 \) to find the factor by which the mass is multiplied to get the spring constant.
Multiply the result from the previous step by the mass \( m = 0.5 \text{ kg} \) to find the spring constant \( k \).
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