A 0.48 kg body undergoes simple harmonic motion of amplitude 8.6 cm and period 0.10 s. (a) What is the magnitude of the maximum force acting on it? (b) If the oscillations are produced by a spring, what is the spring constant?
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- A simple pendulum has a period of 2.5 s. (i) What is its period if its length is made fourtimes larger? (a) 1.25 s (b) 1.77 s (c) 2.5 s (d) 3.54 s (e) 5 s (ii) What is its period if thelength is held constant at its initial value and the mass of the suspended bob is madefour times larger? Choose from the same possibilitiesA tall building is swaying back and forth on a gusty day. The wind picks up and doubles the amplitude of the oscillation.By what factor does the maximum speed of the top of the building increase?By what factor does the maximum acceleration of the top of the building increase?A 0.45 kg block rests on a frictionless horizontal countertop, where it is attached to a massless spring whose k-value equals 19.0 N/m. Let x be the displacement, where x = 0 is the equilibrium position and x > 0 when the spring is stretched. The block is pushed, and the spring compressed, until x₁ = -4.00 cm. It then is released from rest and undergoes simple harmonic motion. (a) What is the block's maximum speed (in m/s) after it is released? m/s (b) How fast is the block moving (in m/s) when the spring is momentarily compressed by 1.70 cm (that is, when x = -1.70 cm)? m/s (c) How fast is the block moving (in m/s) whenever the spring is extended by 1.70 cm (that is, when passing through x = +1.70 cm)? m/s (d) Find the magnitude of the displacement (in cm) at which the block moves with one-half of the maximum speed. |x| = cm
- A 0.478 kg body undergoes simple harmonic motion of amplitude 8.08 cm and period 0.500 s. (a) What is the magnitude of the maximum force acting on it? (b) If the oscillations are produced by a spring, what is the spring constant?A 0.110 kg body undergoes simple harmonic motion of amplitude 7.19 cm and period 0.500 s. (a) What is the magnitude of the maximum force acting on it? (b) If the oscillations are produced by a spring, what is the spring constant?A 0.369 kg body undergoes simple harmonic motion of amplitude 7.85 cm and period 0.250 s. (a) What is the magnitude of the maximum force acting on it? (b) If the oscillations are produced by a spring, what is the spring constant? (a) Number i Units (b) Number i Units
- Two simple harmonic oscillators H1 and H2 of masses on a spring have masses m1 and m2, spring constants k1 and k2, and amplitudes A1 and A2. It is found that the total mechanical energy of H2 equals 4H1. Which one of the following will NOT give this relationship? mị = m2 ; 4k1 = k2 ; A1 = A2 4m1 = m2 ; 4k1 = k2 ; Aı = A2 mi = m2 ; 2kı = k2 ; (v2) A1 = A2 4m1 = m2 ; kı = k2 ; A1 = A2A boy of mass 49.8 kg standing on the end of a diving board depresses it vertically downward a distance of 15.7 cm. By pushing down on the board with a force a little greater than his weight, the boy can depress the end of the board a bit farther. The boy and the board then oscillate up and down. Estimate the period of oscillation, assuming that the force the board exerts is approximately like that of a compressed spring, in other words, that it obeys Hooke's law.A block is attached to a spring with a sping constant of 7.6 N/m and it undergoes simple harmonic motion. The amplitude of the blocks motion is 6.30 cm. When the block is halfway between its equilibrium position and the end point of it's motion, its speed is measured to be 28.9 cm/s. Calculate : (a) the mass of the block, (b) the period of the motion, and (c) the maximum acceleration of the block.
- A spider on a web oscillates horizontally with simple harmonic motion with an amplitude of 2.4 × 10-3 m and period of 0.42 s. (a) State at which point(s) in the oscillation the spider experiences a maximum magnitude of acceleration. (b) Find the maximum magnitude of acceleration that the spider experiences.PhyThe device pictured in the following figure entertains infants while keeping them from wandering. The child bounces in a harness suspended from a door frame by a spring. (a) If the spring stretches 0.250 m while supporting an 8.0-kg child, what is its force constant? (b) What is the time for one complete bounce of this child? (c) What is the child’s maximum velocity if the amplitude of her bounce is 0.200 m?