SIMPLE HARMONIC MOTION
Questions from Breithaupt

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Assume g=10Nkg^-1 

16.1   A small mass attached to a spring oscillates with simple harmonic motion with amplitude of 35 mm, taking 6.5 s to make 20 complete oscillations, calculate
a)    its angular frequency,  rad s^-1
b)    its maximum speed,    m s^-1
c)    its maximum acceleration. m s^-2

16.2   For the small mass of question 16.1, calculate its speed when its displacement from equilibrium is
a) 10 mm, m s^-1
b) 20mm.  m s^-1

16.3   The displacement s of a point object oscillating in simple harmonic motion is described by the equation  s (in mm) = 15cos 10pt (in radians) where t is the time (in s) since passing a fixed point P.
a) What is the amplitude and the time period of the motion? 
amplitude=mm,  time period = s
b) calculate the displacement and speed when t = 0.040 s. 
displacement = mm,  speed = mm s^-1

16.4   The pistons of a 4-cylinder car engine when idling move approximately in simple harmonic motion with an amplitude of 50mm at a frequency of 110 Hz.  Calculate:
     a) the maximum speed of the pistons, m s^-1
     b) the maximum acceleration of the pistons.  m s^-2

16.5   A spiral spring of natural length 300mm is suspended vertically from a fixed point with its upper end fixed. A mass of 0.150 kg is suspended at rest from the lower end of the spring to increase its length to 355 mm. The mass is then pulled down a further distance of 30mm and released from rest so it oscillates about equilibrium. Calculate 
a) the stiffness (i.e. spring constant) k of the spring, N m^-1
b) the time period of oscillations, s
c) the maximum speed and the maximum K.E. of the mass, 
max speed = mm s^-1,   max KE = mJ
d) the maximum and minimum tension in the spring. 
max tension = N,  min tension = N

16.6   When a student pushes down with a force of 200 N on the wing of a car above one of its front wheels, the wing is displaced downwards by 12 mm.
a)  Calculate the stiffness (i.e. spring constant k) of the suspension spring at that wheel. x 10⁴ N m^-1
b) Assuming each wheel is fitted with an identical spring and the mass of the car (with driver) is 600kg; calculate its natural frequency of oscillation.Hz
c)  Estimate the speed at which the car would resonate when travelling over regularly spaced bumps 15m apart.m s^-1