A mass m = 2.8 kg is at the end of a horizontal spring of spring constant k = 490 N/m on a frictionless horizontal surface. The block is pulled, stretching the spring a distance A = 8.5 cm from equilibrium, and released from rest. a) Calculate the period T of the oscillations in seconds.   b)Write an equation for the maximum speed vmax of the block.  c)Write an equation for the maximum acceleration amax of the block.

A yo-yo oscillates up and down like a sine function y(t)=sin(t). a) What is the displacement over the time interval [0,6π]?   b) What is the total distance traveled by the yo-yo over the same time interval?   c) What is the minimum velocity of the yo-yo? Minimum speed?   d) At what part of the cycle is the yo-yo increasing in speed but decreasing in velocity?

You have a stationary mass attached to a compressed spring that is facing horizontal (on a frictionless plane). You give the mass a quick whack with a hammer, such that the mass has an initial velocity of 6.0 m/s. The amplitude of the oscillation of the mass is 4.0 m. How far is the mass from its starting position after 2.0 s? A) 0.50 m B) 0.56 m C) 0.78 m D) 1.0 m E) 1.1 m F) 2.0 m G) 2.3 m H) 4.0 m

A stretched spring is released at time t=0s and allowed to oscillate back and forth on a frictionless surface. The period of harmonic motion is 2s. On the back of this page create the following graphs for one complete oscillation: 1) x-t 2) v-t 3) p-t 4) F,-t 5) a-t 6) K-t 7) U,-t 8) Energy-t Use the space below for any scratch work.

A block of mass m = 2 kg is attached to a spring with force constant k= 500 N/m. The block is subjected to a linear friction force f = -cv. The oscillation graph of the block is illustrated in the graph below. a) Is the oscillator over, under, or critically damped? Justify. b) Determine the period Ta of damped oscillations. c) Deduce the damping parameter y, the angular frequency wa, and the un-damped angular frequency w. d) Determine the constant of friction c. ( e) Write an expression for x(t) and make sure to calculate the numerical values for all parameters in it. Hint: Read the values of xo and vo from the graph, and note that the tangent to the graph is horizontal at t = 0 s.

b) i. A 1.5 kg block is attached to the spring with spring constant k = 300 Nm². The average speed of the block & UTM C i UTM A pendulum with a string of length, = 2.5 m is released from point A as shown % 5UTM 3 UTM & UTM in Figure 3. Determine the speed of the pendulum when reaches the lowest point 5 UTM UTM 40 A A UTM 5UTM &UTM TM A UTM Figure 3

Can you solve it plz

If you increase the value of the oscillating mass, does the frequency of oscillation increase of decrease? Explain.

B1

A spring-mass system with m = 50kg and k = 4000N/m shown in Figure Q3(a). If the mass is released from its equivalent position and results in simple harmonic motion (SHM), (iii)  Explain on how you can reduce the natural frequency of the spring-mass system.