A mass-spring system with mass 2.0kg is oscillating according to x(t) = (2.0)cos(67t) in metres. Find (d) Write and graph the expressions for velocity and acceleration. (e) Calculate the total energy of the system.
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- A 0.50 kg object rests on a frictionless horizontal surface, where it is attached to a massless spring whose k-value equals 25.0 N/m. Let x be the displacement, where x = 0 is the equilibrium position and x > 0 when the spring is stretched. The object is pushed, and the spring compressed, until xi = −4.00 cm. It then is released from rest and undergoes simple harmonic motion. How fast is the object moving (in m/s) when the spring is momentarily compressed by 1.30 cm (that is, when x = −1.30 cm)? How fast is the object moving (in m/s) whenever the spring is extended by 1.30 cm (that is, when passing through x = +1.30 cm)?The acceleration due to gravity in this problem is taken to be g = 9.80 m/ s2 , unless otherwise specified. What is the length of a pendulum that has a period of 0.500 s?A0.366 kg body undergoes simple harmonic motion of amplitude 6.08 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) Number i Units (b) Number i Units
- A 0.500-kg mass is suspended from a string, forming a pendulum. The period of this pendulum is 3.16 s when the amplitude is 1.00 cm. The mass of the pendulum is now reduced to 0.250 kg. What is the period of oscillation now, when the amplitude is 2.00 cm?A metal sphere with a mass 7.00 kg is connected to a spring with a force constant of 200 N/m, and it oscillates horizontally with an amplitude of 2.20 cm. (a) What is the total mechanical energy (in J) of the sphere-spring system? (b) What is the maximum speed (in m/s) of the oscillating sphere? m/s (c) What is the maximum magnitude of acceleration (in m/s2) of the oscillating sphere? m/s²Astronauts in space cannot weigh themselves by standing on a bathroom scale. Instead, they determine their mass by oscillating on a large spring. Suppose an astronaut attaches one end of a large spring to her belt and the other end to a hook on the wall of the space capsule. A fellow astronaut then pulls her away from the wall and releases her. The spring's length as a function of time is shown in the figure (Figure 1). Figure L (m) W 1.4 1.2- 1.0 0.8 0.6 0.4 0.2 0.0 T 3 1 of 1 -t (s) What is her mass if the spring constant is 270 N/m ? Express your answer with the appropriate units. m = 62 kg Submit Part B Correct V = What is her speed when the spring's length is 0.70 m ? Express your answer with the appropriate units. 0.81 Previous Answers Submit Provido Foodbook ΠΑ m sec Previous Answers Request Answer ?
- A mass 566g is attached to an ideal spring. Once set in motion the mass-spring system is a harmonic oscillator. This mass spring system has a total mechanical energy of 226.J. If the oscillation amplitude is 9.318cm, what is the maximum speed of the mass (in)?Assume you have a spring with an elastic constant of 85 N/m, and want it to oscillate once every 0.45 seconds. What mass would you need to attach to the spring?When a 20 N can is hung from the bottom of a vertical spring, it causes the spring to stretch 20 cm. (a) What is the spring constant? (b) This spring is now placed horizontally on a frictionless table. One end of it is held fixed, and the other end is attached to a 5.0 N can. The can is then moved (stretching the spring) and released from rest. What is the period of the resulting oscillation?