23) Fig. 3 shows the displacement – distance graph of a string executing transverse vibrations. Displacement Distance Figure 3
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- 5) A block-spring system oscillates in a simple harmonic motion on a frictionless horizontal table. Its displacement varies with time according to x(t) = 0.2 cos(2t –π /4). The earliest time the particle reaches position x = 0.1 m is1) Is it possible to prescribe the velocity v0, so that the pendulum keeps rotating with alpha = pi/2 Explain clearly why? Given: L, g, and m. 2) After transient motion, the pendulum settles at steady state rotation atalpha = pi/3. Find the initial velocity v0. Given: L, g, m, sin(pi/3) = (squareroot(3)/2), cos(pi/3) = (1/2). [Hint: Use the conservation of energy and the 2nd Newton’s law.]: You are abducted by aliens and find yourself locked in a large room on some strangeplanet. To pass the time, you decide to do some experiments using a ball-and-chain thatyou find on the floor. You make the following estimates:mBALL 7 kg ,mCHAIN 0.5 kg, and CHAIN 2 m .(a) When you hold the free end of the chain above your head and allow the ball to swinglike a pendulum, you use your wristwatch to measure the period asT 4 s. What is theacceleration due to gravity on this planet?(b) If the ball accidentally hits a wall, how long does it take for this jolt in the chain totravel up to your hand?
- Pierce (1948) mechanically measured the frequency (the number of wing vibrations per second) of chirps (or pulses of sound) made by a striped ground cricket, at various ground temperatures. Since crickets are ectotherms (cold-blooded), the rate of their philosophical processes and their overall metabolism are influenced by temperature. Consequently, there is a reason to believe that temperature would have a profound affect on aspects of their behavior, such as chirp frequency. In general, it was found that crickets did not sing at temperatures colder than 60°F or warmer than 100°F. In the following data let X= chirps/sec for the striped ground cricket and Y= temperature in degrees of Fahrenheit. X 19 19.8 18.4 17.1 15.5 14.7 17.1 15.4 16.2 15 17.2 16 17 14.4 Y 71.6 93.3 84.3 80.6 75.2 69.7 82 69.4 83.3 79.6 82.6 80.6 83.5 76.3 a. use two decimal places: Y bar =? b. use two decimal…Somewhere DEEP BELOW THE EARTH's surface, at an UNKNOWN displacement from the Earth's center, a particle of mass m is dangled from a long string, length L; the particle oscillates along a small arc according to the differential equation d^2x/dt^2=-(pi^2/36)x. Here x refers to an angular displacement measured from the vertical and t refers to time. The particle's mass is given by m=3kg. The length of the string is given by L=5 meters. Whenever the particle arrives at a location of x=(pi/12) radians from the vertical, the particle has no instantaneous speed. On both sides of the vertical, that is, x=(pi/12) radians is repeatedly observed to be a 'turning point' for the particle's periodic motion. 1. Draw a clear FREE-BODY diagram of this particle at some arbitrary point during oscillation, making sure to label variables and constants described above. 2. Approximating to three significant digits if necessary, what is the angular frequency of this oscillator on a string? 3. Approximating…A block spring system oscillates in a simple harmonic motion on africtionless horizontal table, its displacement varie with times according to x(t)=0,2cos(2t_3.14/4) the earliest time the particle reaches position x=0,1m is
- A weight is attached to a spring suspended from a beam. At time t = 0, it is pulled down to a point 8 cm above the ground and released. After that, it bounces up and down between its minimum height of 8 cm and a maximum height of 24 cm, and its height h(t) is a sinusoidal function of time t. It first reaches a maximum height 1.4 seconds after starting. (a) Follow the procedure outlined in this section to sketch a rough graph of h(t). Draw at least two complete cycles of the oscillation, indicating where the maxima and minima occur. (b) What are the mean, amplitude, phase shift and period for this function? (Use a phase shift with an absolute value less than the period.) mean 16 amplitude 8 phase shift ___ period 2.8 (c) Give four different possible values for the phase shift. (Enter your answers as a comma-separated list.) _______ (d) Write down a formula for the function h(t) in standard sinusoidal form; i.e. as in the…11) A cylindrical rod of constant radius andconstant shear modulus, G is of length Land located between z=0 and z=L.t=zsin(πZ/2L). call the polar moment of inertia J. The boundary conditions areΦ(0)=0 AND Φ(L)=0 Find Φ(z) and graph (1/GJ)*Φ(Z), and (1/GJ)*(dΦ/dz) ?Angular Impulse and Momentum Principles To apply the principle of angular impulse and momentum to describe a particle's motion. The moment of a force about a point O, fixed in an inertial coordinate system, MO, and the angular momentum about the same point, HO, are related as follows: ∑MO=H˙O where H˙O is the time derivative of the angular momentum, HO=r×mv. Integrating this equation with respect to time yields the following equation: ∑∫t2t1MO dt=(HO)2−(HO)1 This equation is the principle of angular impulse and momentum, and it is often rearranged to its more familiar form (HO)1+∑∫t2t1MO dt=(HO)2 A centrifugal governor consists of a central rotating shaft that has two thin, pin-connected rods attached to it; a heavy sphere caps the end of each rod. (Figure 1) A centrifugal governor mechanically limits an engine's speed. A part of the engine turns the centrifugal governor, and if the speed exceeds a set amount, the height of the spheres decreases the driving force of the engine by…
- Angular Impulse and Momentum Principles To apply the principle of angular impulse and momentum to describe a particle's motion. The moment of a force about a point O, fixed in an inertial coordinate system, MO, and the angular momentum about the same point, HO, are related as follows: ∑MO=H˙O where H˙O is the time derivative of the angular momentum, HO=r×mv. Integrating this equation with respect to time yields the following equation: ∑∫t2t1MO dt=(HO)2−(HO)1 This equation is the principle of angular impulse and momentum, and it is often rearranged to its more familiar form (HO)1+∑∫t2t1MO dt=(HO)2 A centrifugal governor consists of a central rotating shaft that has two thin, pin-connected rods attached to it; a heavy sphere caps the end of each rod. (Figure 1) A centrifugal governor mechanically limits an engine's speed. A part of the engine turns the centrifugal governor, and if the speed exceeds a set amount, the height of the spheres decreases the driving force of the engine by…A block-spring system oscillates in a simple harmonic motion on a frictionless horizontal table. Its displacement varies with time according to x(t) = 0.2 cos(2t - n/4). The earliest time the particle reaches position x = 0.1 m isA child applies a push on his toy car causing it to move horizontally. He controls his applied push such that the x-component Fx varies with the toy’s displacement according to the graph below. What is the total work done by Fx as the toy car moves from x = 0 to x = 15m?