A 1.75 kg mass is attached to a spring and placed on a horizontal, smooth surfac
ID: 1699812 • Letter: A
Question
A 1.75 kg mass is attached to a spring and placed on a horizontal, smooth surface. A horizontal force of 20.1 N is required to hold the mass at rest when it is pulled 0.210 m from its equilibrium position (the origin of the x axis). The mass is now released from rest with an initial displacement of xi = 0.210 m, and it subsequently undergoes simple harmonic oscillations. Calculate the force constant of the spring.
Calculate the frequency of the oscillations.
Calculate the total energy of the oscillating system.
Calculate the speed when the displacement equals one third of the maximum value.
Explanation / Answer
Given that mass of the spring is m = 1.75 kg
horizontal force F = 20.1 N
a ) spring constant k = F / x
= 20.1 N / 0.210 m
= 95.7 N / m
frequency f = 1/2 k / m
= 1/ 2 95.7 N /m / 1.75
= 1.17 Hz
b ) total energy E = 1/2 k A^2
= 1/2 * 95.7 * ( 0.210 m )^2
= 2.110 J
c ) speed v = A^2 - x^2
= k / m
= 95.7 / 1.75
= 7.39 rad /s
v = 7.39 ( 0.210 m)^2 - (1/3 * 0.210 m)^2
= 1.46 m/s
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.