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A machine of mass M rests on a massless elastic floor, as shown in Fig. If a unit load is applied at midspan, the floor undergoes a deflection xst.
Derive the differential equation of motion for the inverted pendulum of Fig, where A cos cat represents a displacement excitation.
A mass-damper-spring system of the type shown in Fig. has been observed to achieve a peak magnification factor Q = 5.
The foundation of the building in Problem below undergoes the horizontal motion y(t) = yo sin wt. Derive the system response.
What maximum vertical height does the ball reach before rolling back down the ramp? What linear distance does the ball travel along the ramp?
Gear A in Problem below is subjected to the torque MA = Mocoswt. Derive an expression for the angular motion of gear B.
The rotor of a turbine having the form of a disk is mounted at the midspan of a uniform steel shaft, as shown in Fig.
Consider the system of Fig. When the support is fixed, y = 0, and the mass is allowed to vibrate freely, the ratio between two consecutive maximum.
Derive the differential equation of motion of the system, then assume small amplitudes and solve for 0(t).
Choose articles related to current epidemiologic trends for infectious diseases and/or the impact of diseases and of the control measures on global populations.
Design a viscous damper so that at the rotating speed w = 4con the force transmitted to the support does not exceed 250 N.
The cam and follower of Fig. a impart a displacement y(t) in the form of a periodic sawtooth function to the lower end of the system.
Solve the differential equation mx¨(t) + cx·(t) + kx(t) = kf(t) by means of a Fourier analysis, where f(t) is the periodic function shown in Fig.
Determine the initial velocity z(0) = v0 for the case in which the initial displacement has the value x (0) = x0 = 2cm.
Determine the natural frequency of the system of Problem below. A cantilever beam in bending is made of two uniform sections, as shown in Fig.
The circular shaft of Fig. has the torsional stiffness GJ(x) = GJ[1-½(x/L)2]. Obtain the equivalent spring constant corresponding to a torque at x = L.
A disk of mass in and radius R rolls without slip while restrained by a dashpot with coefficient of viscous damping c in parallel with a spring of stiffness.
Calculate the frequency of damped oscillation of the system shown in Fig. for the values m =1, 750 kg, c = 3, 500 N . s/m, k = 7 x 105 N/m.
Consider the system of Fig. and plot the response to the initial conditions x-(0) = 2cm, 1(0) = 0 for the values of the damping factor ? = 0.1,1 and 2.
A projectile of mass m = 10 kg traveling with the velocity v = 50 m/s strikes and becomes embedded in a massless board supported by a spring of stiffness.
Derive the equation for small motions y(0 from equilibrium, as well as the natural frequency of oscillation.
Derive the equation for the horizontal translation of the slab and determine the natural frequency.
To determine the centroidal mass moment of inertia lc of a tire mounted on a hub, the wheel was suspended on a knife edge.
A connecting rod of mass m = 3 x 10-3 kg and centroidal mass moment of inertia ic = 0.432 x 10-4 kg m2
A simple pendulum is immersed in viscous fluid so that there is a resisting force of magnitude ca acting on the bob.