2. What would you need to change about that periodic system to change its frequency? For example, a person swinging on a swing-set is periodic motion, and the frequency can be changed by changing the length of the chain attached to the seat.
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The periodic motion is a motion that is repeated in a regular period of time. A cycle is referred to as a complete repetition. And the time taken for each cycle is called a period of the system. The frequency of the system is defined as the number of the cycle completed in a second. So period is the reciprocal of frequency of the system.
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- 2. An object whose mass is 520 g is fastened to the end of a horizontal spring whose spring constant is 78 N/m. The object is pulled 5.0 cm from equilibrium and released. Assume no friction between the object and the floor. (a) What is the angular frequency and the period of oscillation? b) Write the specific equation of motion for this oscillating system, in the form x(t) A cos(cot + )5. A mass of 25 g moves with simple harmonic motion. It has "springiness" of 1.5 N/m and friction causes it to slow down with a damping constant of 250 g/s. Is the system overdamped or underdamped? What would the damping constant need to be for the system to be critically damped?5) A 750 gr block is fastened to a spring with a spring constant of 145 N/m and then pulled 25 cm and released on a horizontal frictionless surface. a) What is the frequency of the motion? b) What is the Period of the motion? c) What is the angular frequency? d) What is the Amplitude? e) Write an equation of the Position as a function of time. f) Write an equation of the Velocity as a function of time. g) Write an equation of the Acceleration as a function of time. h) What is the maximum velocity? i) What is the maximum acceleration?
- 5. A block is attached to a horizontal spring. Find a model for the displacement d as a function of time given the following conditions: a. At time t = 0, the block is pulled to the left 6 cm with a frequency of 2 Hz. W -3-2-1 0 1 2 3 + d b. At time t = 0, the initial displacement is 0 inches (moving to the right), the amplitude is 15 centimeters, and the period is 1 sec.5-3. Below given figure shows a simple oscillator with damping. In this, a mass m is attached to a spring (spring constant k) and a damper with damping force proportional to -bv. The spring and the damper are attached to the walls on the opposite sides of the mass (see Figure). The oscillator can be driven either by moving an attachment point on the damper (Case I) or the end of the spring (Case II). In both cases, the position of the attachment point as a function of time is s(t) = so cos(wat). For BOTH of the above cases, answer each of the following questions. (i). Write the equations of motion of the mass m. (ii). Find the amplitude of steady state solution in terms of given parameters. P Figure: Two weays dn've an oiilator Cae I: mwwo m to Sct) cale II!