Chapter 22, Problem 51P

A block having a weight of 8 lb is suspended from a spring having a stiffness k = 40 Ib/ft. If the block is pushed y = 0.2 ft upward from its equilibrium position and then released from rest. What is the natural frequency of the vibration? Assume that positive displacement is downward.

Determine the oscillation amplitude and frequency of the mass in the figure below for t₁ ≤ t ≤ t₂. Assume that the system is vibrating in a steady-state condition during this time period. What is the frequency of vibration from time t₂ on? F = F₁ sin wt k = 50 N/m 0.5 kg c=1 N-s/m F(t) ky(t) ↓↓ M F, newtons Fo AN ᏁᏁᏁᏁᏁᏁᏁᏁᏁ [y(1) dy(t) dt 8 10 -1₂, when excitation stops 12 14 1, seconds

A 8.6kg body is suspended from a spring of constant k = 6.9kN/m. At time t = 0, it has a downward velocity of 0.5m/s as it passes through the point of static equilibrium. Determine the natural frequency of the system in rad/s. k m. Answer: Next page evious page ce 9Type here to search

A block having a weight of 8 lb is suspended from a spring having a stiffness k = 40 Ib/ft. If the block is pushed y = 0.4 ft upward from its equilibrium position and then released from rest. What is the amplitude of the vibration? Assume that positive displacement is downward

Q1) A dynamic vibration absorber is shown in Figure. This system is representative of many situations involving the vibration of machines containing unbalanced components. The parameters M2 and k12 may be chosen so that the main mass M1 does not vibrate in the steady state when F(t) = a sin wo(t). Obtain the differential equations describing the system. Force F(t) M1 M2

The weight W = 30 lbs. is vertically suspended on a steel wire of length l =50in and of cross-sectional area A = 0.001 in2. Determine the frequency of free vibrations of the weight if the modulus for steel is 30x106 lbs./in 2.Determine the amplitude of this vibration if the initial displacement x 0= 0.01in. and initial velocity v0=1 in/sec

A spring has a spring constant of k=18N/m, hung with a weight of mass m=½ kg. If the load is in an equilibrium position, then it is pulled and released with a speed of 3 m/s, then determine the equation of motion of the object if it does not experience friction or damping.

O O O O m₁ (Automobile) -k₁ (Leaf springs) -m₂ (Wheels and axles) k₂ (Tires) v1=25.87 km/h and v2=110.63 km/h v1=49.69 km/h and v2=194.2 km/h v1-39.53 km/h and v2=124.52 km/h v1=28.63 km/h and v2=116.85 km/h

A 4.0kg body is suspended from a spring of constant k = 3.4kN/m. At time t = 0, it has a downward velocity of 0.5m/s as it passes through the point of static equilibrium. Determine the natural frequency of the system in rad/s. m Answer: Next page rious page P Type here to search