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The motion of a mass tied to a spring is described by the equation x=25cos(3t+6)cm. Given A= 25, K= 2 /meter, determine the mass
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- A mass of 62g is placed on the end of a 3.2cm vertical spring. This causes the spring to extend to 9.9cm. If we then change the mass to 284g, what is the measured length of the spring (in m)?The periodic motion of an object is described by this equation:x = ( 2 / 7 m ) cos( π t / 16 )What is the frequency of the oscillation?Given that the Spring energy is ½ kx2, where x is the displacement of the spring from its equilibrium position, and k is the spring constant, what are the units of k, if the spring energy is in Joules (kg m2/s2)?
- A spring is hanging down from the ceiling, and an object of mass m is attached to the free end. The object is pulled down, thereby stretching the spring, and then released. The object oscillates up and down, and the time T required for one complete up-and-down oscillation is given by the equation T = 2л√/m/k, where k is known as the spring constant. What must be the dimension of k for this equation to be dimensionally correct? O [T] O [T]² O [M] O [M]/[T] O [T]/[M] O [M]/[T]² O [T]²/[M]A spring is hanging down from the ceiling, and an object of mass m is attached to the free end. The object is pulled down, thereby stretching the spring, and then released. The object oscillates up and down, and the time T required for one complete up-and-down oscillation is given by the equation T = 2л√m/k, wherek is known as the spring constant. What must be the dimension of k for this equation to be dimensionally correct? O [T] O [M] O [M]/[T] O [T]/[M] O [M]/[T]² O [T]²/[M]A pendulum has a period of 5.8 s. If you were to transfer this pendulum to the surface of Mars (where g is 3.71 meters per second squared), what would the period (in seconds) be?
- We measure the period of oscillation of a simple pendulum. In successive measurements, the readings turn out to be 2.63s, 2.56s, 2.42s, 2.71s, and 2.80s. Calculate the absolute errors, relative error, or percentage error.The length of an elastic wire is x under a tension of 5 N. Its length is y when the tension is 7 N. If the tension becomes 9 N then the length of the wire will be 7x - 5у (a) 2у — х (b) (c) 7x + 5y (c) 2y + xThe planet Earth, Jupiter, the Moon, and the Sun have the following values: mJ = 1.90x1027kg , mE = 5.97x1024kg , mM = 7.35x1022 kg , mS = 1.99x1030kg RJ = 6.99x107 m , RE = 6.37x106 m, RM = 1.74x106 m , RS = 6.96x108 m dEarth to Moon = 3.60x105 km , dEarth to Jupiter = 588x106m , dEarth to Sun = 150x106 km (a) Find the magnitude of the force of gravity acting on the planet Earth due to the planet Jupiter. (b) Find the potential energy between the planet Earth and the planet Jupiter. (c) Find the acceleration of gravity on the planet Jupiter.
- You have a spring about which you know little, but with experimenting you discover that it extends 1 cm when a mass 41.15 is applied to it. How far would it extend if a mass 79.49 were applied? Give your answer in meters, not cm.Suppose the oscillatory motion of an object can be modeled using the equation s(t) = 7.8sin(3.8t) where time is measured in seconds and distance is measured in inches. Find the number of cycles (oscillations) the object makes per second. (Provide 4 decimal places.)use the model for the period of a pendulum, T, such that T=2pi square root of L/g, where the length ofpendulum is L and the acceleration due to gravity is g. if the acceleration due to gravity is 9.8m/s^2 and the period equals 3s, find the length to the nearest cm. (100 cm= 1m)