1. A 40.2 kg boy jumps on a spring rider causing the frequency to occur at 8.6 Hz. Find the spring constant. 2. A 1211.4 kg car is constructed on a frame supported by 4 springs. Each spring has a spring constant of 20106.8 N/m. If two people riding in the car have a combined mass of 125 kg, find the period of vibration of each spring when a car is driven over a pothole in the road. Assume the weight is evenly distributed.
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. A 40.2 kg boy jumps on a spring rider causing the frequency to occur at 8.6 Hz. Find the spring constant.
2. A 1211.4 kg car is constructed on a frame supported by 4 springs. Each spring has a spring constant of 20106.8 N/m. If two people riding in the car have a combined mass of 125 kg, find the period of vibration of each spring when a car is driven over a pothole in the road. Assume the weight is evenly distributed.
3. A steel wire 1.1 m long with a mass per unit length of 0.0049 kg/m and under a tension of 82 N. Find the longest wavelengths of the sound waves created by the vibrating wire. Assume the speed of sound in the air when the temperature is 26 °C.
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