A 1.0 kg mass is attached to the end of a vertical ideal spring with a force constant of 400 N/m. The mass is set in simple harmonic motion with an amplitude of 10 cm. The speed of the 1.0 kg mass at the equilibrium position is (A) 2 m/s (B) 4 m/s (C) 20 m/s (D) 40 m/s (E) 200 m/s
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- A block rests on a frictionless horizontal surface and is attached to a spring. When set into simple harmonic motion, the block oscillates back and forth with an angular frequency of 6.5 rad/s. The drawing shows the position of the block when the spring is unstrained. This position is labeled "x = 0 m." The drawing also shows a small bottle located 0.080 m to the right of this position. The block is pulled to the right, stretching the spring by 0.050 m, and is then thrown to the left. In order for the block to knock over the bottle, it must be thrown with a speed exceeding vo. Ignoring the width of the block, find vo. x=0m الفيسا 0.050 m 0.080 mWhich of the following forces, acting on a particle of mass m, will not result in simple harmonic motion? The displacement of the particle from the equilibrium position is denoted by x(t). (a) F(t) = -2x2(t) (b) F(t) = +2x2(t) (c) F(t) = +2x(t) (d) F(t) = -2x(t)A 0.36 kg object, attached to a spring with spring constant k= 10 N/m, is moving on a horizontal frictionless surface in simple harmonic motion of amplitude of 0.082 m. What is its speed at the instant when its displacement is 0.041 m? 3.7 m/s 37.4 cm/s 14 m/s 26.5 cm/s
- A spring hangs vertically from a ceiling. The spring constant of the spring is k=15 N/m. A 2kg object has been attached to the spring and the spring has already come to its new equilibrium. Someone pulls the object down by 5cm and releases it at time t = 0s. The spring and object begin to oscillate under simple harmonic motion. Find the total energy of the system, the maximum kinetic energy, the maximum potential energy, and the positions where the maximum energies occur. Answers: 0.01875 J, 0.01875 JA mass is placed on a frictionless, horizontal table. A spring (k=115 N/mk=115 N/m), which can be stretched or compressed, is placed on the table. A 3-kg mass is anchored to the wall. The equilibrium position is marked at zero. A student moves the mass out to x=7.0 cmx=7.0 cm and releases it from rest. The mass oscillates in simple harmonic motion. Find the position, velocity, and acceleration of the mass at time t=3.00 st=3.00 s. x(t=3.00 s)=x(t=3.00 s)= Correct cm v(t=3.00 s)=v(t=3.00 s)= Incorrect cm/sThe length of a simple pendulum is 0.75 m and the mass of the particle (the "bob") at the end of the cable is 0.39 kg. The pendulum is pulled away from its equilibrium position by an angle of 8.9° and released from rest. Assume that friction can be neglected and that the resulting oscillatory motion is simple harmonic motion. (a) What is the angular frequency of the motion? (b) Using the position of the bob at its lowest point as the reference level, determine the total mechanical energy of the pendulum as it swings back and forth. (c) What is the bob's speed as it passes through the lowest point of the swing? (a) Number i 0.58 Units rad/s (b) Number i 0.037 Units (c) Number i 0.435 Units m/s
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