A mass weighing 32 pounds stretches a spring 2 feet.
(a) Determine the amplitude and period of motion if the mass is initially released from a point 1 foot above the equilibrium position with an upward velocity of 6 ft/s.
(b) How many complete cycles will the mass have completed at the end of 4 seconds?
Answer:
Period = 
seconds
8 cycles
Explanation:
A mass weighing 32 pounds stretches a spring 2 feet;
it implies that the mass (m) = 
m= 
= 1 slug
Also from Hooke's Law
2 k = 32
k = 
k = 16 lb/ft
Using the function:
(because of the initial position being above the equilibrium position)
( as a result of upward velocity)
NOW, we have:
However;
means
also implies that:
Hence, 
Period can be calculated as follows:
= 
= seconds
How many complete cycles will the mass have completed at the end of 4 seconds?
At the end of 4 seconds, we have:
cycles
I don't think you mean 'criteria'. I think you mean three occurrences or
observations that indicate the presence of acceleration.
They are:
-- an object is speeding up
-- an object is slowing down
-- the direction of an object's motion is changing .
Any one of these changes is acceleration.
There's a single term that covers them all. It is "change in velocity".
consider the motion in Y-direction
v₀ = initial velocity = 29 Sin62 = 25.6 m/s
a = acceleration = - 9.8 m/s²
t = time of travel
Y = vertical displacement = - 0.89 m
using the equation
Y = v₀ t + (0.5) a t²
- 0.89 = (25.6) t + (0.5) (- 9.8) t²
t = 5.3 sec
consider the motion along the horizontal direction :
v₀ = initial velocity = 29 Cos62 = 13.6 m/s
a = acceleration = 0 m/s²
t = time of travel = 5.3 sec
X = horizontal displacement =?
using the equation
X = v₀ t + (0.5) a t²
X = (13.6) (5.3) + (0.5) (0) t²
X = 72.1 m
d = distance traveled by the center fielder to catch the ball = 107 - x = 107 - 72.1 = 34.9 m
t = time taken = 5.3 sec
v = speed of center fielder
using the equation
v = d/t
v = 34.9/5.3
v = 6.6 m/s
Answer:
v = wavelength * frequency
frequency = 5200 m/s / .2 m = 26000 / sec
20,000 / sec is optimistic for the upper frequency of human hearing
So 26,000 is above the hearing range for human ears
Answer:
the mouth I think
Because: the oesophagus is the throat and the mouth is how the food gets to the oesophagus. might be wrong because I'm not sure about the organ part but I'm pretty sure that's all it could be
