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: Given data, Mass m = 0.20 kg Energy E = 7.50 J Spring constant k = 240 N/m
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Q: The 25 g mass of a 0.7 m long simple pendulum is released when the wire makes an angle of 13 ° with…
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Q: Page 7 of 7 34. A mass-spring system undergoes SHM. The elastic potential energy at maximum stretch…
A: Mass m = 0.20 kg Energy E = 7.50 J Spring constant k=240 N/m
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Q: Page 7 of 7 34. A mass-spring system undergoes SHM. The elastic potential energy at maximum stretch…
A: Given data, Mass m = 0.20 kg Energy E = 7.50 J Spring constant k = 240 N/m
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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.A spring-mass system consists of a spring of stiffness 20 N/mm and a mass 12.74 kg, which can slide on a dry horizontal plane surface with coefficient of friction 0.32. The mass was displaced a distance 39 mm to the right of the frictionless equilibrium position and then released with zero initial velocity. Determine: a) The frequency of vibration.b) The position of the mass after a half cycle.c) The position of the mass after one cycle.d) The reduction of the strain energy in the spring during the first cycle.e) The work done by the friction force during the first cycle.f) The position and time at which the mass stops.(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)
- An undamped oscillator is driven at its resonance frequency wo by a harmonic force F = F, sin wot. The initial conditions are x, = 0 and vo = 0. (a) Determine r(t). (b) If the breaking strength of the 'spring' of the oscillator is 5F., deduce an equation from which the time t, taken to reach the breaking point can be calculated in terms of wo-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 osccilatorA 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 ?