Answered: b) The amplitude b of forced vibration… | bartleby

Related questions

Question

b) The amplitude b of forced vibration in a mechanical system is given by
fo
b =
[(o-o) + 4r2o²2
Show that for
1) 0<<
the
response
is independent of the mass,
ii) for o = @o, the amplitude at resonance depends inversely on the damping constant
r and
i1) for o>> Wo, the response is independent of the spring constant of the system.

Expert Solution

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

A mass of 2 kg on a spring with k = 6 N/m and a damping constant c= 4 Ns/m. Suppose Fo = v2 N. Using forcing function Fo cos(wt), find the w that causes practical resonance and find the amplitude.
A spring with spring constant 50 N/m is hanged from a vertical ceiling. It is then pulled by 30 cm and let it oscillate (ignore air resistance). Which statement is true? O Speed of the mass is maximum at the amplitude O Acceleration is maximum at the amplitude Speed is constant throughout the oscillation Energy is zero at the amplitude MacBook Air
Galileo (17 years old) watched a lamp suspended from the ceiling goefling of the Cathedral in Pisa Italy, as it was swinging back and forth. He discovered that the period of oscillation was the same for large or small amplitudes. If the length of the chain was L, what period did he observe? Suppose the length of the chain ] is L = 44 m. (in s) L Camp A: 6.33 OB: 9.18 OC: 13.31 OD: 19.29 OE: 27.98 OF: 40.57 OG: 58.82 OH: 85.29
While seated on a tall bench, extend your lower leg a small amount and then let it swing freely about your knee joint, with no muscular engagement. It will oscillate as a damped pendulum. as shown is a graph of the lower leg angle versus time in such an experiment. Estimate (a) the period and (b) the timeconstant for this oscillation.
A system with 100g_mass and a spring constant of k=150N/m has a damping constant y=1.1. ASsume the mass was pulled to the right 30 cm at t=0and released. a)Estimate the time at which the amplitude has decayed to ¼ of its initial value. b)Assume the system is connected to a forcing function given by(in Newtons)F(t)=3coswtEstimate the value of the amplitude at resonance.
A particle moves in simple harmonic motion with a frequency of 4.20 Hz and an amplitude of 4.00 cm. (a) Through what total distance does the particle move during one cycle of its motion? cm (b) What is it maximum speed? cm/sWhere does this maximum speed occur? as the particle passes through equilibrium O at maximum excursion from equilibrium O exactly halfway between equilibrium and maximum excursion O none of these (c) Find the maximum acceleration of the particle. m/s2Where in the motion does the maximum acceleration occur? as the particle passes through equilibrium Ⓒat maximum excursion from equilibrium O exactly halfway between equilibrium and maximum excursion O none of these
weight .) A weight of 64 pounds (Recall mx" + Bx' + kx stretches a spring 2 feet. A damping device imparts a damping force 0 and m 32 numerically equal to 16 times the instantaneous velocity. The initial position is x (0) = 2 and the initial velocity is x' (0) = –1 . This is the equation of motion for the mass. -4t x = (-2t – 1) e t -4t O x = (-7t – 2) eAt -2t O x = 2e cos(2t) +e t sin(2t) -4t O x = (7t + 2) e
A 0.480 kg object connected to a light spring with a spring constant of 19.5 N/m oscillates on a frictionless horizontal surface. The amplitude of motion is 3.00 cm. a) Calculate the total energy of the system (in J). [Select ] b) Calculate the maximum speed of the object (in m/s). [ Select ] c) Find the velocity of the object when the displacement is 2.00 cm (in m/s). [ Select ] d) Find the kinetic energy of the system when the displacement is 2.00 cm (in J). [ Select ] e) Find the potential energy of the system when the displacement is 2.00 cm (in J). [ Select ]
A 0.60 kg block rests on a frictionless horizontal surface, where it is attached to a massless spring whose k-value equals 18.5 N/m. Let x be the displacement, where x = 0 is the equilibrium position and x > 0 when the spring is stretched. The block is pushed, and the spring compressed, until x, = -4.00 cm. It then is released from rest and undergoes simple harmonic motion. (a) What is the block's maximum speed (in m/s) after it is released? 1.23 X Mechanical energy is conserved in this system, and the gravitational term remains unchanged (since all motion is horizontal). Write an expression for mechanical energy that includes the kinetic energy and the potential energy of the spring. Which term(s) can be ignored when the spring is compressed and the block at rest? Which term(s) can be ignored when the block is moving at its greatest speed? Use the remaining terms, and the given quantities, to solve for the maximum speed. m/s (b) How fast is the block moving (in m/s) when the spring is…
Asap plz
When taking my pet turkey to the vet, the scale read a mass of 29 kg. The scale consists of a spring that has a force constant value of 36000 N/m. Part (a) What distance did the spring move when the pet turkey jumped onto the scale? d= m Part (b) Assuming that the spring behaves as a simple harmonic oscillator, what is the oscillation frequency of the spring when the pet turkey steps on the scale? f = Hz
A simple harmonic oscillator consists of a mass m attached to a spring with spring constant k, with displacement given by x = A sin(wt + ¢) . Which one of the following is NOT true? O The frequency is independent of the amplitude O The potential energy is a maximum when (wt + 4) = 0 The kinetic energy is a maximum when (wt + ¢) = 0 O The restoring force must be proportional to the negative of the displacement O Increasing the mass will decrease the frequency

SEE MORE QUESTIONS