The 25 g mass of a 0.7 m long simple pendulum is released when the wire makes an angle of 13 ° with the vertical Find: (c) mechanical energy;
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- a uniform rod is 1 m long and has a mass of 10 kg. it is pinned at point a, a frictionless pivot. the rod is released from a rest position 45degrees from the horizontal. the top of an undeflected ideal spring is located at point b to contact the tip of the rod when the rod is horizontal the spring has a constant of 98 kN/m. (c) assume the rod is dropped from the unknown angle, and is 10 rad/s when the rod hit the spring. What will be the maximum deflection of the spring. SHOW COMPLETE SOLUTION.(III) A mass m is connected to two springs, with spring constants k1 and k2, in two different ways as shown in Fig. 14-32a and b. Show that the period for the configura- tion shown in part (a) is given by 1 1 T = 2 %3D m k2. and for that in part (b) is given by m T = 2T %3D V k1 + k2 Ignore friction. vig www.wiw- k1 k2 m (a) k1 k2 w ww w ww m FIGURE 14-32 Problem 25. (b)A simple harmonic osccilator has mass 5.00g makes displacement varies as x=(5.60cm)cos((2.50rad/s)t+π/8). Calculate the maximum kinetic energy of the simple harmonic osccilator
- A block is in SHM on the endof a spring, with position given byx = xm cos(vt+ f). If f = p/5 rad,then at t = 0 what percentage of thetotal mechanical energy is potential energy?A vertical spring-mass system has a 0.6kg weight attached to its end. You stretch the spring 0.4 m away from its equilibrium positon and when it oscillates up and down, it has a frequency of 2.5hz. (a) Calculate the Spring Constant (b) If you increase the distance that you stretch the spring-mass system, expalin how this would affect it's frequency. (c) At what distance from the spring-mass system's equilibrium position does it have the smallest acceleration? Explain your reasoning.The angle (with respect to the vertical) of a simple pendulum is given by e = 0mcos[(5.88 rad/s)t + $]. If at t = 0,0 = 0.0450 rad and de/dt = -0.160 rad/s, what are (a) the phase constant p and (b) the maximum angle em? (Hint: Don't confuse the rate de/dt at which e changes with the w of the SHM.) Pivot point L. e\L S= Le F, cose Fesine- (a) (b) (a) Number i Unit (b) Number Unit >
- (a) (b) (c) (d) The figure below shows a pendulum with length L and the angle 0 from the vertical to the pendulum. It can be shown that 0, as a function of time, satisfies the following nonlinear differential equation d²0 g dt² L where g denotes the acceleration due to gravity. + sin 0 0 For small values of 0 we can assume de dt A 0 sin 0 L such that the differential equation can be considered to be linear. Find the equation of motion of the pendulum with length 750 cm if 0 is initially 15° and its initial angular velocity is = 1 rad/s. What is the maximum angle from the vertical? What is the period of the pendulum (the time to complete one back-and-forth swing)? When will the pendulum be vertical from initial position, that is, 0 = 0 ?A simple pendulum has a 0.020 kg mass which has initial angular displacement of 8.0° hung which is hing from a 12.2 meter massless string. calculate the frequency of the pendulum.