A spring is such that a 2-lb weight stretches it 6 inches. There is a damping force present, with magnitude the same as the magnitude of the velocity. An impressed force (2sin8t) is acting on the spring. If at t = 0, the weight is released from a point of 3 inches below the equilibrium point, find its position for t > 0.

Q: Problem 4.5 A cart of mass M slides freely (no friction) on horizontal tracks. Hanging from the cart…

A: A cart of mass M slides freely No function on elements horizontal track,hanging from the cart is a…

Q: A seismic instrument is used to find the magnitude of vibration of a machine tool structure. It…

A:

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: 4. For small angles of oscillation, find the frequency of oscillation of the system shown in…

A:

Q: A Locomotive starts from rest and pulls a train, weighing 20 X 106 N down a 1per cent grade. The…

A:

Q: 3.10. If the shafts shown in Fig. P3.4 have modulus of rigidity G1 and G2, derive the differential…

A:

Q: An electric motor with a mass of 20 kg is placed in the middle of a beam that is jointly connected…

A: Given: Mass of the rotor m=20kg Speed of the rotor ω=20rad/s Eccentricity e=0.020m Solution: Maximum…

Q: 3. The stiffness of a helical spring is such that it stretches 1 mm per every 1.5N of load. Find the…

A: Given: 1.5 N per 1 mm Mass, m = 6.5 kg To find: Number of vibrations it will make per minute

Q: 2. Determine the equivalent damping of the system.

A: Given Data⇒

Q: Q6. The natural frequency of a spring-mass system is found to be 2 Hz. When an additional massof 1…

A: A spring mass system given if mass m and spring constant k Natural frequency = 2 HzIf mass m+1 and…

Q: weight of mass 2 kg is placed on a long vertical spring with spring constant k = 20. The damping…

A:

Q: If we attach an object weighing 8 lb to a spring, it stretched the latter by 1 ft. We attach a…

A: Given data: Here, Wso represents the weight of the object attached to spring, W represents the…

Q: If the stiffness of the spring is increased to 16 times and mass is reduced to 1/4th times the…

A: Let us take, Original stiffness = k1 Original mass = m1 New stiffness = k2 New mass = m2   From the…

Q: T1= 0.62 s T2= 0.54 s K1= 2440 n/m

A:

Q: The natural frequency of a spring mass system is 2 Hz, When an additional mass of 1kg is added to…

A: The natural frequency of spring is ωn=kmk=2m⋯⋯⋯(1) New stiffness of the spring mass system is (k')…

Q: Determine a natural frequency of vibration as a function of k₁, k₂. g and W of a spring-mass system…

A:

Q: a 15 kg mass, a 300 N/m stiffness spring is used. An initial 60-centimeter displacement is applied…

A: The position of the mass is given by Y(t) = A*Cos(wt).

Q: 3. An undamped spring-mass system has a mass that weighs 48 lb and a spring constant 0.5 lb/in. The…

A: This question is related to the spring-mass system. The elastic vibration wherever there's no…

Q: If mass of 5 kg is attached to a spring with k = 5 N/m and c = 10Ns / m. At t = 0 the mass is 0.1 m…

A: Given, Mass, m=5 kg Spring constant, K=5 N/m Damping constant, C=10 Ns/m at t=, x=-0.1 and v=0.2 m/s

Q: A 40lb weight is stretched to the end of a spring. The spring is stretched 6in. Find the…

A:

Q: For the following system, obtain the mathematical model (Hint: Use superposition principle and…

A:

Q: F 0.5 S 0 UBC Engineering N A block of a mass of 6 kg and a spring with a k value 30 as shown in the…

A: Mass of block, m=6 kgSpring constant, k=30 N/mCompression, x=0.5 mApplied force, F=60 NKinetic…

Q: A simple pendulum of length L is set to oscillate in simple harmonic motion. The bob gravitational…

A:

Q: The natural frequency corresponding to the spring mass system 1 and 2 are W 1 and W2 respectively,…

A:

Q: Use Cramer's rule to determine the solution of the system (2 – k)æ1+kx2 = 4 kai+(3 – k)x2 = 3 300 lb…

A:

Q: 4. Find the equivalent spring constant of the system shown. 00000

A: The figure for system of spring connected in parallel and series is given below,

Q: A belt drives a pulley of 200mm diameter such that the ratio of tensions in the tight side and slack…

A:

Q: The 30kg cylinder causes a static deflection of 50mm in the coiled spring. If the cylinder is…

A:

Q: 4.25 An automobile, having a mass of 1000 kg, runs over a road bump of the shape shown in Fig. 4.49.…

A: To Find : The response of automobile Given :The mass of the automobile is The speed of the…

Q: Problem 6: An object of mass 2 kg is attached to a spring of stiffness 200 N/m on a horizontal…

A:

Q: You have a prototype Slinky with a lump of coal at the end. This forms a damped spring-mass system.…

A: Here Given:- m=1 k=3 b=1

Q: 2. Find the k equivalent of the system, if each spring has a spring constant of 20 lb/in except for…

A:

Q: k2 k3 m - 13-

A:

Q: Damian’s car weighs 2000kg. The spring has a natural unstretched length of 2m and a spring constant…

A: Given: To find: extension of spring

Q: 3. The maximum velocity attained by the mass of a simple harmonic oscillator is 10 cm/s, and the…

A:

Q: A mass of a 2 slug, when attached to a spring, causes an elongation of 2 ft in this spring and then…

A: The mass is m=2 slug The elongation in spring is 2 ft. The external force is f(t) = 8 sin4t. The…

Q: Find the set of initial conditions such that each mass oscillates: a) at the first natural…

A:

Q: Instruction: Find the radial frequency of the system using matrix. The final answer should be…

A:

Q: A 8-lb weight is hung on the lower end of a coil spring suspended from a beam. The weight comes to…

A: Given : W = 8 lb x = 4 in x0 = 6 in F(t) = 8 cos5t To find : Displacement function

Q: When spinning at 500 rotations per minute two washing machines produce two sinusoidal forces with…

A: Given Data: washing machines rotation n=500 rpm Two sinusoidal forces with same maximum amplitude…

Q: A part of a machine has a reciprocating component which is simple harmonic, making a 200 complete…

A:

Q: Q2/ The out - of - balance of a machine rotor is equivalent to 5 kg at 10 mm radius in one plane A,…

A: Mass of the rotor (m) = 5 kg Radius of the one plane A = 10 mm AB = 375 mm Need to determine the…

Q: Activity 2.4- Newton's Second Law Problems Use the free body diagram method to solve the following…

A: The mass of the ball, M = 60 gram = 0.06 kgThe bouncing speed, vo = 15 m/sThe angle, θ = 20ᵒThe…

Free Damped Vibrations

Free vibration is a type of vibration in which the external force is removed after giving the initial displacement to a body/system. In other words, in this type of vibration, force is applied at the initial displacement of the system, and after the initial displacement, force is removed, and the system vibrates at the natural frequency.