A 0.12 kg body undergoes simple harmonic motion of amplitude 8.5 cm and period 0.20 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 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| = cmA particle moves in simple harmonic motion with a frequency of 3.00 Hz and an amplitude of 5.00 cm. (a) Through what total distance does the particle move during one cycle of its motion? (b) What is its maximum speed? Where does this maximum speed occur? (c) Find the maximum acceleration of the particle.
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- A mass of 8.0 kg hangs from a spring attached to the ceiling. The spring has a spring constant of 500 N/m and it stretches 15.7 cm from its mean position. A student grabs the spring, applies a force and stretches it a further 6.7 cm downwards. The block is released and initially accelerates upward before undergoing simple harmonic motion. Calculate the initial vertical acceleration of the mass. (Units: m/s? , to 2 sig figs)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.