Find the product of the complex numbers z1 = (1 + 2i) and z2 = (3 — 4i) and express the result in the form Aeiθ

Q: Determine the natural frequency of the spring-mass system as shown in Figure. The values of spring…

A: When a system is disturbed from its equilibrium position and is left free after disturbance, the…

Q: (2) Find the equivalent spring stiffness for the vibrating system shown in Fig 2. If kl -k3 - ks -…

A: Write the given data. k1=k3=k5=2kk2=k4=k6=k

Q: Q. Show by an example that Kharitonov's Theorem does not hold when the stability region is the…

A: If all four Kharitonov polynomials of a continuous-time interval polynomial are stable, it is…

Q: The mass of the passenger car is 1660 kg, of which 60% is on the front axle. At the front, the…

A: Given, Mass of passenger car,M=1660kg

Q: (i) Thermal distortions and vibrations do not perturb smaller devices as much as large ones because…

A: Correct options are -  (i) option A the resonant vibrations of a system are inversely proportional…

Q: A system subject to sinusoidal excitation is shown in the Figure below: m X, X, X and is modelled as…

A: Given: Natural frequency of the vibration: →ωn=11 rad/s And damping ratio: →ζ=0 Maximum excitation…

Q: Question 3: What is the speed of the mass at the equilibrium position, which makes a simple harmonic…

A: Given: Stiffness of the spring (k)=16N/m Amplitude of vibration (x)=50cm or 0.050m Mass (m)=0.25kg

Q: H. W - 1 k2 Determine the natural frequency of the system shown beside. b g ki

A: By using newton method  Now take the moment about A  IAθ¨+K1a2θ+K2b2θ=0IAθ¨+K1a2+K2b2θIA=0

Q: Which following differential equation is correct for the shown pendulum system oscillation: (a) O ö…

A:

Q: 2. Which vibration category that can represent the image given below x(t) k f(t) m C Free vibration…

A:

Q: A particle is attached to a spring that creates a vibration with a frequency of 8 Hz. Determine the…

A: Given:

Q: A) Determine the natural frequency of the torsional system shown below. (Take the shear modulus as…

A: Given, Diameter of left shaft = d1 = 1 inLength of left shaft = l1 = 12 inDiameter of right shaft =…

Q: solid steel shaft 4 m long is stressed to 60 MPa when twisted through 3 degrees. (a) Given that G =…

A:

Q: The combination consists of three resistors (10, 15, and 50) kQ respectively, if these resistors are…

A:

Q: Q2 : (Section A) A engine valve assembly shown by figure. If J is the inertia caused by the…

A: NOTE:- there are two different questions in above image which is not correlated to each other.As per…

Q: 4) Answer one only (A) An end of a combined string has a linear mass density of 8.00 kg/m, whereas…

A: Given data: -  The linear mass density of first string is ρ1 = 8.00 kg/m. The linear mass density…

Q: Consider the system shown in the figure and the following numerical values: L= 100 in El = 10° Ib-in…

A:

Q: a period of 0.3 s. The time needed by the block to move (for the first time) from position x A to x…

A: To complete one cycle pendulum traveled 4 times wrt to its mean position therefore, Divide the time…

Q: 1. When the displacement of a machine is given by x(t) = 18cosl0f, where x is measured in…

A:

Q: 2DOF system as shown in figure below, M1=m, M2=2m, k1 =5k, k2=10k. 1. Write down the equations of…

A:

Q: 19- The zero energy of a simple harmonic oscillator is

A: Zero Energy of Simple harmonic oscillator : The zero Energy of oscillator is the lowest allowed…

Q: The equation of motion for a damped vibration is given by 6x + 9x + 27x = 0. The damping %3D

A: Given:The equation of damping vibration,6x¨+9x˙+27x=0,

Q: 1. Determine the equivalent spring constant. ki k2 ks 1000

A: The equivalent stiffness of springs can be find out by following ways: 1: springs 1 and 3 are…

Q: 置一 with spring constants e= wn is the positive direction. fhess matrix K - e the external force…

A:

Q: The string of a piano is made of music wire. The wire has a mass of 150 grams and a length of 1.5 m.…

A:

Q: Find the linearization of the equation: 0 = ( +m )* + mg sin 0

A: m+JR2θ¨+mgsinθ=0sinθ≈θm+JR2θ¨+mgθ=0

Q: solve please by lagrang method to find the eqation of motion and to find the frequencies and mode,…

A: a=255 mm b=100 mm L= 400 mmM=1.1 kgm=.995 kgk=5 Nmm or 5000 Nm

Q: . A helical spring of stiffness k is cut into two halves and a mass m is connected to the two halves…

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Q: 4) Using the energy method, obtain the equation and natural frequency of the system shown in Figure…

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Q: An object attached to a coiled spring is pulled down a distance 8 units from its rest position and…

A: Given data: T=5 secondsa=-5 Need to determine the equation that relates to the displacement of the…

Q: Q2 : (Section A) A engine valve assembly shown by figure. If J is the inertia caused by the…

A: For solution refer below images.

Q: 2.2 A spring-mass system has a natural period of 0.21 sec. What will be the new period if the spring…

A: Given data:

Q: The shock absorbers on a car are using to falling-off down the vibrations of the car. Do the number…

A:

Q: 7. The velocity as a function to the displacement for a horizontal motion in a medium which the…

A:

Q: Vibrations Engineering: A rope of a pendulum has a length of 2 meters. What is the natural…

A: Mechanical Vibration

Q: In the shown figure, let m1 = 1 kg, m2 = 2 kg, k1 = k3 = 100 N/m and k2 = 200 N/m. Write the…

A: Draw the free-body diagram of the block 1 and 2,

Q: Identify the degree of freedom of the following system 2. 2. 2m 2A

A: Data gven in the question:-we know 1 spring       = 1 one binary joint so we have toconvert the…

Q: 2 - A particle is subjected simultaneously to two SHMS of the same frequency and in the same…

A: Given, a1=1.5 mma2=2.5 mm The phase of the second component relative to the first SHM, ϕ=400

Q: A device with a mass of 1000 kg is placed on top of the suspension, whereby the springs are…

A: Given data: The mass of the device is m=100 kg The compression of spring is x=4 mm=4×10-3 m

Q: A device with a mass of 370 kg is placed on top of the suspension, whereby the springs are…

A: Given data: The mass of the device is m=370 kg The deflection of spring is x=4 mm=0.004 m

Q: 2) The rotation of the flywheel is governed by w = 2Vt where w is in rad/s and t is in sec. 0 = 3…

A: Given: Rotation of the flywheel is governed by: ω =2t dθdt = ω =2t dθ = 2t*dt  integrate both sides;…

Q: Q2: For the system shown in Figure (2) x denotes the absolute displacements of the mass m and y…

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Q: 300 N 12 mm 24 mm B D E 24 mm 460 mm 96 mm | 300 N 24 mm

A:

Q: 5. When the harmonic oscillator depends on the direction and its restoring force is independent on…

A: Solution.jpg

Q: 1- Finding the values of the critical displacement (x) of the slide with different values of (theta)…

A: Given: x=r(1-cosθ+(sin2θ2n))v=dxdt=rω(sinθ+sin2θ2n)a=dvdt=rω2(cosθ+cos2θ2n) r= 25 mm l=150  mm n=l/r…

Q: Question 5 The figure below shows a ballistic pendulum, which is used to measure the velocity of…

A: Given:m=0.02 KgVo=5 KgL=2 mθ=10°

Free undamped vibrations

Whenever an object/system displaces in either side of its equilibrium position with the help of an external/internal means, then the object/system moves regularly or randomly on both sides of its equilibrium position. This motion is called vibration. Generally, there are three types of vibration: longitudinal vibration, transverse vibration, and torsional vibration.