1.An object has a mass of m = 647 g. It is attached to a spring which has a spri

Question

1.An object has a mass of m = 647 g. It is attached to a spring which has a spring constant of value k = 65 N/m. At time t = 0 the object is pulled to a distance of 28.1 cm from its equilibrium position (which you may choose conveniently at x = 0). The surface on which the object moves is frictionless.

What is the total energy of the system?

Express the result in the unit [J] and to three significant figures. If you must use scientific notation, please enter as follows: e.g. 0.000123 = 1.23E-4. Only answer in numerical values, no units. For negative numbers, leave no space between the negative sign and the number: e.g. right: -1.00, wrong: - 1.00.

2.)The vibration of the tympanic membrane in the human ear (eardrum) can be described as a harmonic motion. Assuming a mass of 20.6 mg and a period of vibration of 1.72 ms, what is the natural vibration frequency of the membrane?

Express the result in the unit [Hz] and to three significant figures. If you must use scientific notation, please enter as follows: e.g. 0.000123 = 1.23E-4. Only answer in numerical values, no units. For negative numbers, leave no space between the negative sign and the number: e.g. right: -1.00, wrong: - 1.00.

Explanation / Answer

1. Given      Mass of the object , m = 0.647 kg      Spring constant , k = 65 N/m      The displcement of the object is , x = 0.281 m      The total energy of the system is       E = mgx + 1/2kx^2          = 0.647 kg * 9.8 m/s^2 * 0.281 m + 0.5 *65 N/m * (0.281 m)^2      E = 4.347 J 2. Period of vibration of the membrane , T = 1.72 *10^-3 s      Frequency of the vibrating membrane is , f = 1/T                                                                       = 1/ (1.72 *10^-3 s)                                                        f = 581.395 Hz

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