0.6 cm 1.5 cm 0.975 cm 1.2 cm
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- In a science museum, a 130 kg brass pendulum bob swings at the end of a 14.7 mm -long wire. The pendulum is started at exactly 8:00 a.m. every morning by pulling it 1.2 mm to the side and releasing it. Because of its compact shape and smooth surface, the pendulum's damping constant is only 0.010kg/s. a. At exactly 12:00 noon, how many oscillations will the pendulum have completeted? b. What is the amplitude at noon?The human eardrum responds to sound by vibrating. If the eardrum moves in simple harmonic motion at a frequency of 2.88 kHz and an amplitude of 0.132 nm, what is its maximum speed of vibration?The midpoint of a guitar string demonstrates simple harmonic motion with motion following the form x(t) = A sin (wt +ϕ). It has an angular frequency of w = 2.65 x 103 s-1 and an amplitude of A=1.50 mm. The phase constant is ϕ= pi/2. What is the maximum magnitude of the acceleration of the string?
- A mass m hangs from a spring of spring constant k and oscillates in simple harmonic motion about its equilibrium point. In terms of m and k, what would be the length of a pendulum with the same period as this mass-spring system? ○ 2лmg/k mg/2xk mg/2k Ⓒ2mg/k O mg/kThe midpoint of a guitar string executes simple harmonic motion with motion following the form x(t) = A sin(wt + p). It has an angular frequency of w = 2.65 × 10³ s-¹ and an amplitude of A = 1.50 mm. Take the phase constant to be p = π/2.Your car rides on springs, so it will have a natural frequency of oscillation. Figure P14.48 shows data for the amplitude of motion of a car driven at different frequencies. The car is driven at 20 mph over a washboard road with bumps spaced 10 feet apart; the resulting ride is quite bouncy. Should the driver speed up or slow down for a smoother ride?
- All spiders have special organs that make them exquisitely sensitive to vibrations. Web spiders detect vibrations of their web to determine what has landed in their web, and where. In fact, spiders carefully adjust the tension of strands to “tune” their web. Suppose an insect lands and is trapped in a web. The silk of the web serves as the spring in a spring-mass system while the body of the insect is the mass. The frequency of oscillation depends on the restoring force of the web and the mass of the insect. Spiders respond more quickly to larger—and therefore more valuable—prey, which they can distinguish by the web’s oscillationfrequency. Suppose a 12 mg fly lands in the center of a horizontal spider’s web, causing the web to sag by 3.0 mm. If the web were vertical rather than horizontal, how would the frequency of oscillation be affected?A. The frequency would be higher.B. The frequency would be lower.C. The frequency would be the same.IC-3 A 167 gram mass is vibrating about its equilibrium position on the end of a spring as shown in problem SHM-8. While vibrating, the mass is observed to have a maximum speed of 0.500m/s and a maximum acceleration of 6.00m/s. At t0 the mass is at the equilibrium position with a velocity to the left. a) Find the numerical values for the angular frequency o and the amplitude of the motion xm. Hint: think about how Vm and xm are related. b) Find the value of the spring constant of the spring. c) The position of the block is described by x Xmcos(@t+0,). Find all possible values of 0, and then explain how to determine the value of 0, that corresponds to the given conditions. 99+ hpA pendulum is formed by taking a 1.5 kg mass and hanging it from the ceiling using a steel wire with a diameter of 1.1 mm. It is observed that the wire stretches by 0.05 mm under the weight of the mass. What is the period of oscillation of the pendulum?
- A 36.0-g object is hung vertically from a spring and set to oscillate. It takes 6.95 seconds to complete 10 full oscillations. Instead, if a 26.0-g object is hung and set to oscillate, how long does it take to complete 10 full oscillations?A pair of hoop earrings is in the form of peace signs and each earring can be made to oscillate with simple harmonic motion about the point where the earring is attached to the hook that goes through the ear lope. The earrings are made of cylindrical silver wire having a density of 10.2 g/cm3 and a diameter of 0.15 cm. Each earring can be thought of as consisting of a ring that is 1.5 cm in diameter, a central vertical rod that is 1.2 cm in length and two diagonal rods, each 0.6cm in length as shown in the diagram above. The distance from the pivot point of the earring to the center of mass of each diagonal rod is 0.975 cm. Based on this information, determine the period of this physical pendulum.5. A pair of hoop earrings is in the form of peace signs and each earring can be made to oscillate withsimple harmonic motion about the point where the earring is attached to the hook that goes throughthe ear lope. The earrings are made of cylindrical silver wire having a density of 10.2 g/cm3and adiameter of 0.15 cm. Each earring can be thought of as consisting of a ring that is 1.5 cm in diameter, acentral vertical rod that is 1.2 cm in length and two diagonal rods, each 0.6 cm in length as shown in thediagram above. The distance from the pivot point of the earring to the center of mass of each diagonalrod is 0.975 cm. Based on this information, determine the period of this physical pendulum.