18Assume that there's no damping. 17.=A mass of one kg is attached to a spring with constant k = 4 N/m. An external force F(t)- cos wt - 2 sin wt n is applied to the mass. Find the displacement y for t > 0 if w equals thenatural frequency of the spring-mass system. Assume that the mass is initially displaced 3 mabove equilibrium and given an upward velocity of 450 cm/s.18.An object is in simple harmonic motion with frequency wo, with y(0) = yo and y' (0) = vo. Findits displacement for t > 0. Also, find the amplitude of the oscillation and give formulas for thesine and cosine of the initial phase angle.

Answered: Image /qna-images/answer/a0b48f19-e4d8-47e1-9a71-794c33a8f633.jpg

Answered: 17. A mass of one kg is attached to a…

Similar questions

How do you know whether the angular frequency depends on the mass, spring constant, and amplitude?
5. A mass of 25 g moves with simple harmonic motion. It has "springiness" of 1.5 N/m and friction causes it to slow down with a damping constant of 250 g/s. Is the system overdamped or underdamped? What would the damping constant need to be for the system to be critically damped?
2-calculate the average kinetic energy Ek , < n | Ek | n > and the potential energy V for SHM.
What is transient in vibration?
2. Solve the motion of the damped harmonic oscillator driven by a force Fext(t) = Fo cos² wt
Chapter 6 Applications of Linear Second Order Equations 288 6.2 Exercises 4. A 96 lb weight stretches a spring 3.2 ft in equilibrium. It is attached to a dashpot with damping constant c-18 lb-sec/ft. The weight is initially displaced 15 inches below equilibrium and given a downward velocity of 12 ft/sec. Find its displacement for t > 0
B7
22) Solve this question without any mistake.
4) A variable-speed electric motor, having an unbalance, is mounted on an isolator. As the speed of the motor is increased from zero, the amplitudes of vibration of the motor have been observed to be 0.55 inches at resonance and 0.15 inches at speeds much greater than resonance. Find the numerical value of the damping ratio of the isolator.
3. Below given figure shows a simple oscillator with damping. In this, a mass m is attached to a spring (spring constant k) and a damper with damping force proportional to -bv. The spring and the damper are attached to the walls on the opposite sides of the mass (see Figure). The oscillator can be driven either by moving an attachment point on the damper (Case I) or the end of the spring (Case II). In both cases, the position of the attachment point as a function of time is s(t) = so cos(wat). For BOTH of the above cases, answer each of the following questions. (i). Write the equations of motion of the mass m. (ii). Find the amplitude of steady state solution in terms of given parameters. P Figure: Two weays dn've an oiilator Cae I: mwwo m to Sct) cale II!