A mass m is connected to one end of a horizontal spring whose spring constant is k. Assuming that the mass of the spring may be neglected and that the mass rests on a frictionless surface, derive an expression for its circular frequency w, natural frequency f, and period T. k www m

A machine part of mass 1.95 Kg vibrates in a viscous medium. Determine the damping coefficient when a harmonic exciting force of 24.46 N results in resonant amplitude of 1.27 cm with a period of 0.20s.

A mass-spring system of mass m = 0.2 kg and elastic constant k = 5 N/m is immersed in a viscous fluid which exerts a damping force on the system. Furthermore, the system is subjected to a harmonic forcing of intensity F_0 = 10 N and frequency w rad/s. The value of the damping constant is b = 1.5 Ns/m. If the system starts at rest and in its equilibrium position, find: a) the frequency w for which the system is in resonance; b) Make a graph of position v/s time where the amplitude and period of the system can be seen explicitly if the frequency w is equal to twice the resonance frequency; c) Make a graph of amplitude v/s frequency where the maximum frequency and the resonance frequency of the system can be seen explicitly.

According to a source THEORYO F VIBRATION WITH APPLICATIONS FOURTHEDMON W I L L IAMT.THOMSON

A mass of 21.5 kg is vibrating freely at the end of 3 springs connected in parallel. The spring constants are 112.2 N/m, 412.8 N/m and 1051.5 N/m. Determine the frequency in Hz of the vibration. (Express answers to 2dp) Answer:

Consider a damped mass-spring system with mass 3 kg, spring constant 10 N/m, and damping coefficient 5 kg/s. At t = 0, the mass is displaced a distance 0.7 m from equilibrium and released from rest. How long (in seconds) would you have to wait until the mass completes ten ocillations? In other words, how long do ten complete oscillations take?

A 15 kg block hangs from a spring with a spring constant of 12 kN/m.  The block is initially held so that the spring is unstretched.  If the block is released, what is the natural circular frequency of the block’s vibration?

A compact object with a mass of 8.80 kg oscillates at the end of a vertical spring with a spring constant of 1.60 ✕ 104 N/m. The motion is damped by air resistance, and the damping coefficient is b = 3.00 N · s/m. (a) What is the frequency (in Hz) of the damped oscillation?   Hz (b) By what percentage does the amplitude of the oscillation decrease in each cycle?  % (c) Over what time interval (in s) does the energy of the system drop to 5.00% of its initial value?  s (d) What If? The atmosphere of Venus is 50 times thicker than that on Earth. If the effect of air resistance on Venus is represented by b = 150 N · s/m, recalculate the answers for parts (a) to (c) for this system if it is set in motion in the atmosphere of Venus. What is the frequency (in Hz) of the damped oscillations?  Hz What is the percentage decrease in amplitude in each cycle?  % What is the time interval (in s) for the energy to drop to 5.00% of its initial value?  s

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A particle undergoes damped harmonic motion. The spring constant is 100 N/m; the damping constant is 8.0 x 10-3 kg m/s, and the mass is 0.050 kg. If the particle starts at its maximum displacement, x = 1.5 m, at time t = 0, what is the particle's position at t = 5.0 s? -1.5 m -0.73 m Om 0.73 m 1.5 m