Use the following information. Michael Kasha, of Florida State University, used physics and mathematics to design a classical guitar. He used the model for the frequency of the vibrations on a circular plate v = 2.6t / d2 sqrt(E/p) where v is the frequency (in vibrations per second), t is the plate thickness (in millimeters), d is the diameter of the plate, E is the elasticity of the plate material, and ? is the density of the plate material. For fixed values of d, E, and ?, the graph of the equation is a line, as shown in the figure. Estimate the plate thickness when the frequency is 600 vibrations per second. (Round your answer to one decimal place.) mm
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.
Use the following information. Michael Kasha, of Florida State University, used physics and mathematics to design a classical guitar. He used the model for the frequency of the vibrations on a circular plate
where v is the frequency (in vibrations per second), t is the plate thickness (in millimeters), d is the diameter of the plate, E is the elasticity of the plate material, and ? is the density of the plate material. For fixed values of d, E, and ?, the graph of the equation is a line, as shown in the figure.
Estimate the plate thickness when the frequency is 600 vibrations per second. (Round your answer to one decimal place.)
mm
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