Pr2. A mathematical pendulum swings with angular amplitude a (a « 1), its period is T. By what factor does the period of the pendu- lum change if it is suddenly surrounded by two perfectly elastic walls (see figure)? The walls are arranged symmetrically, their angular distance is a.
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- A physical pendulum is made by cutting a circular lamina from a plywood sheet. The radius is 25 cm and the mass is 5 kg. The lamina is suspended on a nail through a hole drilled 15 cm from the center of the circle, and the pendulum is set in motion. a) What is the period of the pendulum? b) Where is the center of oscillation for this pendulum?Q4. An ideal mass-spring system is oscillating horizontally. When the mass is at its maximum distance from the equilibrium position, which of the following statements about it are true? (This is a multi-select question. You may select one or more options.) Its speed is at its maximum. Its kinetic energy is at its minimum. Its total mechanical energy is zero. The spring's potential energy is at its maximum. Its acceleration is non-zero.The pendulum shown below consists of a uniform disk with radius r = 2.35 cm and a mass of 410 grams. The disk is supported in a vertical plane by a pivot located d = 1.75 cm from the center of the disk. Pivot• d R. a. What is the frequency of oscillation if the disk is displaced by a small angle and released? Hz b. What is the frequency of oscillation if the mass of the disk is and then displaced by a small angle and released? Hz
- Q3: A pendulum consists of a mass m and a massless stick of length I. The pendulum support oscillates horizontally with a time dependent position given by x(t) = A cos(ot); (See Figure) x(1) m At anytime, the position of the pendulum mass m is given by (X, Y) = (x(t) + / sine, - / cose) Then (a) Write the Lagrangian of the pendulum. (4 Marks) (b) Write the Euler-Lagrangian equation for 8. (3 Marks) (c) What is the equation in (b) in small-angle limit (→0)? (2 Mark)Atoms in a solid continuously vibrate due to thermal energy. At room temperature, the amplitude of these atomic vibrations is about 1.4 x 10-11 meters, and their frequency is about 1.1 x 1012 hertz. What is the maximum speed of a vibrating atom? Include units in your answer. PLEASE ANSWER IN HANDWRITING THANK YOU!!!6. The pendulum shown is a nonlinear dynamic system. Get a dynamic system linear around 0 = 0° for this dynamic system and the transfer function corresponding linearized. Consider m = 10kg; L = 0.5m. Also, note that in the axis of rotation there is a torsion spring of stiffness with k = 100N*m / rad. m,L k 2m
- КА kB = wwwwww.. Lo = ellele Spring A N/m ниши N/m LA The two springs A and B depicted above are made of different materials and have different spring constants kд and k. The springs happen to have the same natural length Lo = 0.1 m. m When a mass m = 0.46 kg is hung from spring A, spring A oscillates for a short time then settles down to a stretched length LA = 0.23 m. When an identical mass is hung from spring B, spring B settles down to a stretched length LB = 0.4 m. What are the spring constants kд and kg of these springs, measured in N/m? Lo Spring B LB mmmmmmI drive a Nissan Leaf to work. With the e-pedal on, the motor recovers energy through braking very aggressively. I need about 7 KW-hour to come to school if I use mostly the freeways. That’s about 5 KW-hour if I take mostly local streets. From the energy perspective, can you offer an explanation to explain this difference?the question is about Oberbeck's pendulum. The mass m0 is 95.5 g Diameter of shave 87 mm Height 440 mm 4. What radius of the central sheave is necessary to make the fall time exactly 6 s, if the same pendulum with weights at R=150 mm is used? o 261 mm o 7.25 mm o 0.989 mm o 0.994 mm o 9.745 mm o 9.697 mm
- A mathematical pendulum swings with angular amplitude α (α ≪ 1), its period is T . By what factor does the period of the pendulum change if it is suddenly surrounded by two perfectly elastic walls (see figure)? The walls are arranged symmetrically, their angular distance is α.Grandfather clocks are designed so they can be adjusted by moving the weight at the bottom of the pendulum up or down. Suppose you have a grandfather clock at home that runs slow by 6 seconds per minute, or 10%. Which of the following adjustment(s) would make it more accurate? (This is a multi-select question. You may select one or more options.) O Decrease the amplitude of swing by 10%. Decrease the length of the pendulum to approximately (0.9)2 times the original length. Take away mass from the weight because the period is inversely proportional to square root of the mass. Increase the length of the pendulum to approximately (1.1)2 times the original length. Add more mass to the weight because the period is proportional to square root of the mass. Increase the amplitude of swing by 10%.5). The motion of a particle is defined by the follouing equations: ex = x-2y and dt dy =5x-y with x(0)=2 and yco) =-1 dt a. Find x(t) and yit) b. If xlt) and yct) are perniodic, find their amplitudes and peiods. Co which apaph represents the moton best? 3. う人 フイ NIETHER A 2.