according to the HOMEWORKLIB RULES we have to answer only one question at a time. sol-2
2. For the simple pendulum shown in Figure 2, the nonlinear equations of motion are given by θ(t)...
P4. A clock keeps time using the periodic motion of a simple pendulum. The pendulum consists of a string of length L and a bob of mass m-5.00 kg attached to the end of the string. The pendulum has a period T-1.00 s. The initial angle (0) at 0 is equal to 0.175 rad. The bob is released from rest (i.e. -0) at -0. The angle between the string and the vertical is given by the equation: e-a cos (or...
(1 point) Suppose a pendulum of length L meters makes an angle of θ radians with the vertical, as n the figure t can be shown that as a function of time, θ satisfies the differential equation d20 + sin θ-0, 9.8 m/s2 is the acceleration due to gravity For θ near zero we can use the linear approximation sine where g to get a linear di erential equa on d20 9 0 dt2 L Use the linear differential equation...
I need help with c). Question 2 The simple pendulum, discussed in week 4 and lab session 4, has the equation of motion f0/dt2_0? sin θ 9-(g/L)I/2. with The total energy of the pendulum is constant during the motion, and is given by _mgL cos θ, wher dt is the angular speed of the motion in radians per second. Consider the simple pendulum with initial conditions θ(0) and u(0)-wi, 0 i.e. starting from the vertically down position with an initial...
I need help with C Question 2 The simple pendulum, discussed in week 4 and lab session 4, has the equation of motion f0/dt2_0? sin θ 9-(g/L)I/2. with The total energy of the pendulum is constant during the motion, and is given by _mgL cos θ, wher dt is the angular speed of the motion in radians per second. Consider the simple pendulum with initial conditions θ(0) and u(0)-wi, 0 i.e. starting from the vertically down position with an initial...
The motion of a pendulum bob with mass m is governed by the equation mL0" (t) + mg sin θ (t)-0 where L is the length of the pendulum arm, g 3 and θ is the angle (in radians) between the pendulum arm and the vertical. Suppose L 16 ft and the bob is set in motion with (0 1 and 0' (0)--3. Find the second degree Taylor polynomial P2(t) that approximates the angular position θ(t) of the bob near...
2. The nonlinear pendulum is governed by the equations du g sin e dt dt L Solve using a) forward Euler and b) backward Euler for L = 9m, At 0.1s, vo = 0.6m s-1 and 0, 0. Integrate for 25s and plot v as a function of t. Comment on your results. Note that if a scheme is implicit, you may have to iterate 4o convergence at each time step. Use your own judgement on how best to do...
Ch. Ex. 73- The angular acceleration of a simple pendulum is given by 2 out of 4 attempts The angular acceleration of a simple pendulum is given by sin 0, where g is the acceleration of gravity and L is the length of the pendulum cord. Let the length of the pendulum cord be L-1.6 m. II e-3.3 rad/s when o -16°, determine the maximum value of0 achieved by the pendulum.
Question 2 The pendulum shown in Figure 2 consists of a concentrated mass m attached to a rod whose mass is small compared to m. The rod's length is L. The equation of motion for this pendulum is Suppose that L 1 m and g 9.81 m/s2. Use MATLAB to solve this equation using symbolic and numerical techniques for, θ(t) for two cases: , θ(0)-0.5 rad and, θ(0)-0.8 rad. In both cases 0(0) 0. Figure 2- A pendulum [3 marks]...
Consider the simple pendulum shown in the figure. The ball can be assumed to be a concentrated mass of 10 kg attached to a massless rod of length 1=50 cm. a) Determine the period of oscillation of the simple pendulum b) If 8, = 12º and ., = 0 , find 0(t).
2. The position of the motion of the bob in a simple pendulum in radians is given by θ(t)--3 cos(nt + π) What is the amplitude, frequency, and period of the motion? 3. A man enters a tall tower needing to know its height. He notes that a long pendulum extends from the ceiling almost to the floor, and its period is 12 s. How tall is the tower?