A particle of mass 2.5 kilograms is attached to one end of a light, inextensible string of length 75 cm. The other end of this string is attached to a point A. The particle is also attached to one end of an elastic string of natural length 30 cm and modulus of elasticity 2. N. The other end of this string is attached to a point B, which is 60 cm vertically below A. The particle is set in motion so that it describes a horizontal circle with centre B. The angular speed of the particle is 8 rads-1 Find 2, giving your answer in terms of g.
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- 0. A mass of 0.42 kg, attached to a horizontal ideal spring of force constant 38 N/m, undergoes simple harmonic without friction at an amplitude of 5.3 cm. (a) What total distance does mass cover during a single oscillation? [ANS: 21.2 cm] (b) What is the maximum energy of the mass - spring system? [ANS: 0.053 J] ( c) Determine the maximum speed of the mass? [ANS: 0.50 m/s] (d) What is the speed of the mass when the displacement is 4.0 cm? [ANS: 0.33 m/s]One end of a string is attached to an object of mass M, and the other end of the string is secured so that the object is at rest as it hangs from the string. When the object is raised to a height above its lowest point and released from rest, the object undergoes simple harmonic motion with a frequency f0. In a second scenario, the length of the string is cut in half before the object undergoes simple harmonic motion again. What is the new frequency of oscillation of the object in terms of f0?Problem 5: Near the top of the Citigroup Center building in New York City, there is an object with mass of 3.2 × 105 kg on springs that have adjustable force constants. Its function is to dampen wind-driven oscillations of the building by oscillating at the same frequency as the building is being driven- the driving force is transferred to the object, which oscillates instead of the entire building. Part (a) What effective force constant should the springs have to make them oscillate with a period of 1.8 s in N/m? Part (b) What energy is stored in the springs for a 2.2 m displacement from equilibrium in J?
- A 2.00 kg frictionless block attached to an ideal spring with force constant 315 N/m is undergoing simple harmonic motion. When the block has displacement +0.200 m, it is moving in the negative x-direction with a speed of 4.00 m/s. Find (a) the amplitude of the motion; (b) the block’s maximum acceleration; and (c) the maximum force the spring exerts on the block.A spring of negligible mass stretches 3.46 cm from its relaxed length when a force of 5.4 N is applied. A 0.8 kg particle rests on a frictionless horizontal surface and is attached to the free end of the spring. The particle is displaced from the origin to x=5. cm and released from rest at t=0.(f) Determine the displacement x of the particle from the equilibrium position at t=0.50 s(g1) Determine the velocity of the particle when t=0.50 (g2) Determine the acceleration of the particle when t=0.50 sNear the top of the Citigroup Center building in New York City, there is an object with mass of 4.00×105 kg on springs that have adjustable force constants. Its function is to dampen wind-driven oscillations of the building by oscillating at the same frequency as the building is being driven—the driving force is transferred to the object, which oscillates instead of the entire building. (a) What effective force constant should the springs have to make the object oscillate with a period of 2.00 s?(b) What energy is stored in the springs for a 2.00-m displacement from equilibrium?
- A vertical wire 2.1m long and of 0.0042 cm2 cross sectional area has a Young’s modulus of 2.00 x 1011 Pa. A 4.0 kg object is fastened to its end and stretches the wire elastically. If the object is now pulled down a little and released, the object undergoes vertical single harmonic motion. Find the period of its vibration.A 0.60 kg block rests on a frictionless horizontal countertop, where it is attached to a massless spring whose k-value equals 23.0 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 xi = −4.00 cm. It then is released from rest and undergoes simple harmonic motion. Have answer to a need answers to b-d (a)What is the block's maximum speed (in m/s) after it is released? 0.25 m/s (b) How fast is the block moving (in m/s) when the spring is momentarily compressed by 2.10 cm (that is, when x = −2.10 cm)? ____________________ m/s (c) How fast is the block moving (in m/s) whenever the spring is extended by 2.10 cm (that is, when passing through x = +2.10 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 simple harmonic oscillator consists of a 1.20 kg block attached to a spring. The block is ocillating back and forth along a straight line on a frictionless horizontal surface. A plot of the position of the block (in cm) as a function of time (in seconds) is shown below. What are (a) the spring constant of the spring and (b) the maximum speed and maximum acceleration of the block? (c) What is the velocity of the block at t = 1.50 s? 4. 3- 2- -2- -3- -4- -5+ 0.2 0.4 0.6 0.8 Position (cm)