1- An oscillating system consists of a mass m1 = 1.5 kg on a smooth surface, which is attached to an elastic spring whose stiffness is characterized by the constant k = 22.0 N / m. If initially the block is displaced from the spring balance position by a distance 10.0 cm to the right and free from rest. Based on previous information: (a) Determine the angular frequency ω of the oscillation if it behaves like a simple harmonic oscillator; (b) Express the position of the block as a function of time according to initial conditions mentioned above.
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
1- An oscillating system consists of a mass m1 = 1.5 kg on a smooth surface, which is attached to an elastic spring whose stiffness is characterized by the constant k = 22.0 N / m. If initially the block is displaced from the spring balance position by a distance 10.0 cm to the right and free from rest. Based on previous information:
(a) Determine the angular frequency ω of the oscillation if it behaves like a simple harmonic oscillator;
(b) Express the position of the block as a function of time according to initial conditions mentioned above.
2- For the same previous oscillation system, oscillating harmoniously, there is a block of mass m2 = 0.80 kg that moves from right to left quickly 2.5 m / s, and collides with the spring mass system just when the block of mass m1 is at its maximum position at right. If the blocks stick together and the movement continues oscillating gear by the action of the same spring:
(a) What physical magnitude is preserved during the collision and why?
(b) Determine the angular frequency of the movement oscillation development of the set of blocks;
(c) Express the position of the set of blocks according to the according to the initial conditions mentioned above previously.
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