Scientists have developed a clever way to measure a mass of virus using a spring. A cantilever beam in the scanning electron microscope image below is like a diving board, except that it is extremely small (a couple of micrometer). The cantilever beam with mass m can oscillate (imagine a vibrating diving board) and it can be modeled as a spring with a spring constant k. What you can measure experimentally is the frequency of oscillation of the cantilever first without the virus (f1) and after the virus had attached itself to the cantilever (f2). (a) Find the mass of virus from f1 and f2 (assume that we don’t know the spring constant k) (b) Suppose the mass of cantilever is 10.0 * 10^-16 g and a frequency of 2.00 * 10^15 Hz without the virus and 2.87 * 10^14 Hz with the virus. What is the mass of the virus?
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.
Scientists have developed a clever way to measure a mass of virus using a spring. A cantilever beam in the scanning electron microscope image below is like a diving board, except that it is extremely small (a couple of micrometer). The cantilever beam with mass m can oscillate (imagine a vibrating diving board) and it can be modeled as a spring with a spring constant k. What you can measure experimentally is the frequency of oscillation of the cantilever first without the virus (f1) and after the virus had attached itself to the cantilever (f2). (a) Find the mass of virus from f1 and f2 (assume that we don’t know the spring constant k) (b) Suppose the mass of cantilever is 10.0 * 10^-16 g and a frequency of 2.00 * 10^15 Hz without the virus and 2.87 * 10^14 Hz with the virus. What is the mass of the virus?
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