A damped harmonic oscillator with m = 10 kg, k = 250 N/m, and c = 6 driving force given by F, cos ot, where F= 48 N. (a) What value of o results in steady-state oscillations with maximum ar condition: %3! %3D

A mass, spring and a damper system is subjected to an external harmonic excitation of 200cos5t (N). Find the response for the following givens: K =4000 N/m. m = 10 kg, c = 40 N.s/m, x, = 0.1 m and vo = 0 m/s Select one: O e0112(-0.005sin0.9595t 0.0345cos0.9595t) + 0.0347sin(5t-3.058) O 0.45 e-2 cos (21.899t + 0.02671) + 0.066 cos(20t-0.1325) O .0.0345 e2t cos (19.899t + 0.02671) + 0.066 cos(5t-0.1325) O .0.0345 e-2t cos (19.899t + 0.02671) + 0.066 cos(5t-0.1325) TOSHIBA

ASAP

Find the free-vibration response of a spring-mass system subject to Coulomb damping for the following initial conditions x(0) = 0.5 m, *(0) = 0. Data: m= 10kg, k = 200 N/m, µ = 0.5. Q1 . ...

Given an oscillator of mass 2.0kg and spring constant of 180N/m, what is the period without damping?  Use numerical methods to model this oscillator with an additional friction force equal to where c is a positive damping constant.  Using c=5.0, what is the new period of oscillation.  What about for c=10? Assume initial position is 0.2m and initial velocity is zero. Please find the period using the position versus time plot and use the first full cycle of the motion.

Q.5 Use normal mode analysis to find the natural frequencies of the system shown below: The specific values of m2 =6, k2 =150 m2 k2 m = 2 kg %3D k = 40 N/m

Given the lumped parameter model of a second-order system mÿ+by+ky = F(t), what is the natural frequency and damping ratio, respectively, of the system? A. √/k/m, b/2√m D. √k/m, b/2√mk F. k/m, √/mk/b B. √k/b, m/ 2bk G. b/k, √/b/2mk C. F/k, y/mbk H. 2π/m, 2/b√mk 1. /k, mkb E. √k/m, 1/2√√mk J. √m/bk, 1/√2

C Fill the correct answer in the blank space 1 The center of mass fem for three unit mass particles system equal: ... 2 The vector bi + 3j - k is perpendicular to the vector i + 2j-3k, then value of (b) is *** 3 If the damping frequency is wo/2 and the applied frequency is wo/4. Then tan of the phase angle equals; .... 4 Lagrangian approach is based on 5 Inertial term due to ............. of coordinate system. 6 A planet become faster in orbit around the sun when the sun.

: An undamped oscillator has a natural frequency of a rad/s. Damping is added to the system to give a damping factor equal to 0.30 s¬1. Find the corresponding Q – value and frequency of damped oscillations. 3 For a Damped Simple Harmonic Oscillator, wo? – w² = 10-w,?, where (w) is the frequency of DHO. Find Q, and the logarithmic decrement (A) of the system. If wo = 106 rad/s, Q, = 5 × 10² and m = 10-10kg, calculate the stiffness, and resistive constant (b) of the system. S For a driven damped oscillator, show that the energy dissipated per cycle by a frictional force F4 = bv : ngular frequency (w) is given by: E = nbwA². 1

A simple harmonic motion as shown in Figure Q1(a) has a maximum velocity of(1) m/s with (4) second(s) of the period of oscillator. If the mass is releasedwith an initial displacement of (8) mm, (i) Define appropriate equation of ?, ?̇ and ?̈for simple harmonic motion(ii) Determine the amplitude, initial velocity, maximum acceleration, and phaseangle of the system