A mass is placed on a frictionless, horizontal table. A spring (k=108 N/m) which can be stretched or compressed, is placed on the table. A 5 kg mass is attached to one end of the spring, the other end is anchored to the wall. The equilibrium position is marked at zero. A student moves the mass out to x= 5 cm and releases it from rest. The mass oscillates in SHM. (a) Determine the equations of motion in terms of the amplitude 'A', the angular velocity 'w', and the time 't'. Use the initial conditions to find the value of & in the equations. Hint: Use the equation editor (orange button in the answer box) and find w in the greek letters. DO NOT USE numerical values for A and w for part (a). For example, a equation could be x(t)= Asin (wt). x(t)= v(t)= a (t)= m m/s m/s² (b) Calculate for this spring-mass system. @= rad s (c) Find the position, velocity, and acceleration of the mass at time t=3.2 s. Use w up to 4 significant figures in the calculation. Note: Should you set your calculator in degree or radian mode? Position: x = Velocity: v= Acceleration: a = m m S m $2

A mass is placed on a frictionless, horizontal table. A spring (k=108 N/m) which can be stretched or compressed, is placed on the table. A 5 kg mass is attached to one end of the spring, the other end is anchored to the wall. The equilibrium position is marked at zero. A student moves the mass out to x= 5 cm and releases it from rest. The mass oscillates in SHM. (a) Determine the equations of motion in terms of the amplitude 'A', the angular velocity 'w', and the time 't'. Use the initial conditions to find the value of & in the equations. Hint: Use the equation editor (orange button in the answer box) and find w in the greek letters. DO NOT USE numerical values for A and w for part (a). For example, a equation could be x(t)= Asin (wt). x(t)= v(t)= a (t)= m m/s m/s² (b) Calculate for this spring-mass system. @= rad s (c) Find the position, velocity, and acceleration of the mass at time t=3.2 s. Use w up to 4 significant figures in the calculation. Note: Should you set your calculator in degree or radian mode? Position: x = Velocity: v= Acceleration: a = m m S m $2

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter12: Oscillatory Motion

Section: Chapter Questions

Problem 1OQ: Which of the following statements is not true regarding a massspring system that moves with simple...

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Which of the following statements is not true regarding a massspring system that moves with simple harmonic motion in the absence of friction? (a) The total energy of the system remains constant. (b) The energy of the system is continually transformed between kinetic and potential energy. (c) The total energy of the system is proportional to the square of the amplitude. (d) The potential energy stored in the system is greatest when the mass passes through the equilibrium position. (e) The velocity of the oscillating mass has its maximum value when the mass passes through the equilibrium position.
In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the expression x=5.00cos(2t+6) where x is in centimeters and t is in seconds. At t = 0, find (a) the position of the piston, (b) its velocity, and (c) its acceleration. Find (d) the period and (e) the amplitude of the motion.
We do not need the analogy in Equation 16.30 to write expressions for the translational displacement of a pendulum bob along the circular arc s(t), translational speed v(t), and translational acceleration a(t). Show that they are given by s(t) = smax cos (smpt + ) v(t) = vmax sin (smpt + ) a(t) = amax cos(smpt + ) respectively, where smax = max with being the length of the pendulum, vmax = smax smp, and amax = smax smp2.
A 200-g block is attached to a horizontal spring and executes simple harmonic motion with a period of 0.250 s. The total energy of the system is 2.00 J. Find (a) the force constant of the spring and (b) the amplitude of the motion.
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A mass is placed on a frictionless, horizontal table. A spring (k=100N/m) , which can be stretched or compressed, is placed on the table. A 5.00-kg mass is attached to one end of the spring, the other end is anchored to the wall. The equilibrium position is marked at zero. A student moves the mass out to x=4.0 cm and releases it from rest. The mass oscillates in SHM. (a) Determine the equations of motion. (b) Find the position, velocity, and acceleration of the mass at time t=3.00 s.
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