A spring-mass system with m = 50kg and k = 4000N/m shown in Figure Q3(a). If the mass is released from its equivalent position and results in simple harmonic motion (SHM), (i) Starting from a free body diagram, derive the equation of motion. (ii) Determine the natural frequency.  (iii) Explain on how you can reduce the natural frequency of the spring-mass system.

Q: A mass-spring system oscillates on a frictionless horizontal surface in simple harmonic motion with…

A:

Q: 35. A block of mass m = 2 kg is attached to the ends of two identical springs and rests on a…

A: First, calculate the natural frequency in rad/sec, then in Hz.

Q: Q2\ Amass is suspended from a spring system as shown in fig. Determine the natural frequency of the…

A: Solution 2 - In this problem the spring with spring constant k2 and k3 are in parallel arrangement.…

Q: 6.14. Assuming small oscillations, derive the differential equations of motion of the two degree of…

A:

Q: Consider a mass-spring system that oscillates with frequency w when there are no external forces…

A: Initial position = 8 cm Initial velocity = 4 cm/s time t = 9 s Hammer force = 7 grs cm/s2

Q: A disc of mass M = 2 kg, and radius R = 20 cm is connected to a spring at a point at a distance r =…

A:

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: Equivalent stiffness of a beam system is 105 N/m and mass of the object resting on the beam system…

A:

Q: system in the figure with m1 = 1.2 kg, m2 = 2.7 kg, k1 = 10 N/m, k2 = 20 N/m and k3 = 30 N/m. Find…

A:

Q: An object of mass m = 0.2 kg is hung from a spring whose spring constant is 80 Nm-1. The body is…

A: Given Data  Mass, m=0.2Kg b=4 N/m K=80 N/m Ans(A)…

Q: Figure Q3(b) shows a uniform bar AB of mass = 8 kg hinged at point C. Point A is connected to a…

A: Given data: The spring constant is k=500 N/m The mass is m=8 kg The small angle is θ=3.5°…

Q: 4. What are the frequencies of vibration of a mass m = 5 kg (i) on a spring with modulus k, = 20…

A: Free Body diagram

Q: An object of mass m = 0.2 kg is hung from a spring whose spring constant is 80 Nm-1. The body is…

A: Given, m=0.2kg. k=80N/m, Restoring force  Resistive force  1.  Differential equation of the motion…

Q: A spring is stretched 200 mm by a 15-kg block. If the block is displaced 200 mm downward from its…

A: To Find :  The phase angle. Given :  The mass of block is  m=15 kg. The downward velocity is  v=0.75…

Q: Two identical objects of mass m = 0.2 (kg) are connected to two identical springs with spring…

A: m = 0.2 kg k = 320 (N/m) The natural frequency of the system when the mass is moved at an angle of θ…

Q: An electrical switch gear is supported by a crane through a steel cable of length 4 m and diameter…

A:

Q: A railroad bumper is designed as a spring in parallel with a viscous damper. What is the bumper's…

A:

Q: 6.6. Determine the differential equations of motion of the two degree of freedom system shown in…

A:

Q: Consider an ideal SPRING-MASS SYSTEM with a block of mass m attached to a movable end of a…

A: Given data Spring-mass system with a block of mass m attached.Spring constant = k It undergoes…

Q: An electrical switch gear is supported by a crane through a steel cable of length 4 m and diameter…

A:

Q: 2) A block of mass m is attached to a spring with force constant, k and oscillate at a frequency f.…

A: The initial frequency of the spring-mass system is given as, f=12πkm Here, k, and m represent spring…

Q: A mass m is attached to two identical springs having spring constant k as shown in the figure. The…

A: Here, Two springs of stiffness k are in parallel connection. The equivalent stiffness of parallel…

Q: The mass of the system shown in figure below is moved 13 mm to the right and released Numerical…

A:

Q: musical string instrument, has a string with a linear mass density of 5 g/m, vibrating in its fifth…

A:

Q: shaft of 50 mm diameter and 0.5m long is fixed at one end and other end carries a disc of mass 500…

A: given:diameter of the shaft D=50mmlength of the shaft l =0.5mmass of the disc m=500kgthe radius of…

Q: A spring-mass system with m = 50kg and k = 4000N/m shown in Figure Q3(a). If the mass is released…

A: (i) Free body diagram Equation of motion…

Q: A .6kg block is hung from a spring with a force constant of 25 N/m. Calculate the displacement of…

A: Data given -  Mass of the block = 0.6 kg  Force constant k = 25 N/m

Q: Consider a place where the gravity is one-fourth the gravity on Earth (g' = g/4), then the frequency…

A: Given data g' = g/4

Q: 6.6. Determine the differential equations of motion of the two degree of freedom system shown in…

A:

Q: 3.18. For the system shown in Fig. P3.7, let m =0.5 kg, k1 = k2 = k3 = 1000 N/m, and c= 10N - s/m.…

A: The Answer is Below

Q: A mass-spring system oscillates on a frictionless horizontal surface in simple harmonic motion with…

A: Given : Amplitude, A = 0.1 m   In Simple Harmonic Motion, The motion of the mass-spring system…

Q: The mass spring system shown in Figure Q3 consists of two masses and three springs that are arranges…

A: 3.1 Given: m1 = 18 kg m2 = 9 kg k1 = 1350 kN/m k2 = 675 kN/m k3 = 1575 kN/m   From the FBD,…

Q: A mass of 1 kg is suspended by means of 3 springs as shown in figure. The spring constant K, K, and…

A: Given:K1=1 kN/mK2=3 kN/mK3=2 kN/mm=1 kg

Q: A mass-spring system oscillates on a frictionless horizontal surface in simple harmonic motion with…

A:

Q: A washing machine has 60 kg mass, and 15 cm tub radius. Machine dries the unbalanced 3 kg laundry by…

A: (a) The angular velocity of the washing machine is The magnitude of the dynamic force can be…

Q: given in the figure a mass of three arcsand a transformation element, you can find the equivalence…

A: given data m=2 kg, k=10N/m, c=0.1 Ns/m

Q: (b) Consider the system as shown in figure task 2b k, = 2 N/cm k1 = 1.5 N/cm k1 = _N/cm k1 = 0.5…

A:

Q: A rod 4 feet long is rigidly fixed at one end and has a mass of 45 pounds concentrated at the other…

A:

Q: A mass m is attached to two identical springs having spring constant k as shown in the figure. The…

A: Given data: The stiffness of the springs is k. The magnitude of the mass is m.

Q: A light ball of mass m is tightly stretched by strings with initial tension, T, as shown in the…

A: Given data: Mass = m Tension = T Need to natural frequency.

Q: A uniform bar of mass m= 7 kg and Length L= 1 m, pivots at point O and is supported by a spring at…

A:

Q: Consider a simplified model for a single-story building as shown in the figure below. Assume that…

A: considering the system

Q: 2. In the system shown in Figure 2, the massless rigid rod of length l = l4 + l2 is pivoted at point…

A:

Q: A mass-spring system oscillates on a frictionless horizontal surface in narmonic motion with an…

A:

Q: Two identical springs of spring constant 7580 N/m are attached to a block of 0.245 kg as shown in…

A:

Q: k = 2.4 N/cm, W = 24N, L1 = 12cm, L2 = 8cm The total weight of the object shown in the figure is W.…

A:

Q: For the system shown in figure below, derive the differential equation of motion for small…

A:

Q: Consider a place where the gravity is one-fourth the gravity on Earth (g' = g/4), then the frequency…

A:

Forced undamped vibrations

In mechanical engineering, vibration is expressed as the term that occurs due to an object's backward and forward movement about a point of equilibrium. Generally, there are three types of vibrations which are,