Y sin ot 2. The upper end of a uniform rod receives a motion Y sin...
uniform rod of mass m is supported by a pin at A and a spring at B. 1 given a small sideward displacement and released: a) Write clearly the equation of motion for the simple harmonic motion. b) Determine the natural period of vibration. e) Determine the natural frequency of vibration B sin 20 = 2 sin 0 cos
7. The uniform rod of mass m is supported by a pin at A and a spring at B. If B is given a small sideward displacement and released: a) Write clearly the equation of motion for the simple harmonic motion. b) Determine the natural period of vibration. c) Determine the natural frequency of vibration. А е L BMW sin 20 = 2 sin cos e
Determine the longitudinal free vibration of a uniform rod clamped at one end and free at the other with a constant force acted on the free end suddenly released at the time t = 0.
3. 2090] Consider a uniform bar of Young's modulus E, cross-sectional area A, moment of inertia density p, length L, with an attached end mass, m, connected to a rigid wall via a linear spring of spring constant, k, see Figure. Let the longitudinal vibration of the bar be Wa.f). (a) [4] Write down the boundary conditions. m E, p Boundary condition at x 0 Boundary condition at x L (b) [81 Derive the equation for the natural frequency (c)...
The mass of the uniform slender steel rod, shown in Figure 2, is 3 kg. The system is set in motion with small oscillations about the horizontal equilibrium position shown. (i) Determine the position x for the slider such that the system period is 1 s. (ii) When the pivot is replaced by a built-in support that restricts any rotation at O and the spring is moved to the right-hand end with the 1.2 kg mass removed, calculate the frequency...
3. A damped harmonic oscillator is driven by an external force of the form mfo sin ot. The equation of motion is therefore x + 2ßx + ω x-fo sin dot. carefully explaining all steps, show that the steady-state solution is given by x(t) A() sin at 8) Find A (a) and δ(w).
A pendulum made of a uniform rod with a length of 70 cm is set into harmonic motion about one end. 1) Calculate the period of its motion.
Problem 3.(30 pts) Derive the equation of motion and find the steady state response of the system shown below for rotational motion about the hinge O for the following data: a 0.25 m, b-0.5m, m, k (You can assume that gravitational force is balanced against the static deflection of the springs) F(t) = Fo sin (ot Uniform rigid bar, mass m M.
A cylindrical fuel rod 50mm in diameter has a uniform internal heat generation of ??1̇ = 7*107 W/m3 . Under steady-state conditions, the temperature distribution is ??(??) = ?? + ????2, where T is in Celsius, ?? is in meters, ?? = 750°C, and ?? = -5.40*105 °C/m2 . The fuel rod properties are k=25 W/(m K), density= 1100 kg/m3 , and cp = 750 J/(kg K). (a) Determine the heat transferred (in Watts) at r=0 (centerline) and r=ro (outer...
418. The e spring k and the dashpot c of the accompanying diagram are fastened together at A; x represents the absolute displacement of m, and y is the abso- lute displacement of the point A. The motion o (a) Construct the free-body diagram for m. (b) Write the differential equation of motion for m (c) Obtain the solution for the steady-state motion of m. (d) Determine the relation for the impressed force at A. A is defined by y-...