At the instant shown, aQ of the point Q of the rotating disk is directed as indicated and has a magnitude of 10m/s2. Determine the speed vp of the point and a in this instant
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
15.6
At the instant shown, aQ of the point Q of the rotating disk is directed as indicated and has a magnitude of 10m/s2. Determine the speed vp of the point and a in this instant.
![15,4 The gear A of the system shown executes 200 rev over a time interva
6 rad/s2. Determine vD. VE. ap, and a of the ponts D
Plane Kinematics
of Rigid Bodies
15.3 At the instant shown, the gear A rotates with O- 2 radie
B rotates with ap
E at this instant.
and fhe
while its angular velocity is being increased from 300 rpm
constant rate a. Determine a, and At.
to 900 rpm
4 in.
60°
6 in.
0.2 m
0.3 m
A
Fig. P15.5 and P15.6*
Fig. P15.3* and P15.4
A circular disk rotates about the point O as shown. At the instant shou
point P moves with vp = 0.9 m/s ↑ and ao of the point Q of the disk is di
dicated. Determine a of the disk and the magnitude of ao at this instant
15.5
rad/s2
as
15.6* At the instant shown, a, of the point Q of the rotating disk is directei.
indicated and has a magnitude of 10 m/s". Determine the speed vp of the pOint
and a of the disk at this instant.
15.7 A small object P rests on a horizontal disk as shown. At the time t = 0
disk accelerates at a constant rate a. = k rad/s from rest until t = 5 s. then
rotates freely without any angular acceleration. It is known that P will start to sla
on the disk when its resultant acceleration exceeds 3 m/s. Determine the maxim
radial distancer for which sliding of P on the disk will not occur.
g. P15.7
15.8 The gears A, B, and C, of radii ra = 500 mm, rB = 200 mm,
rc = 150 mm, respectively, all rotate about fixed axes parallel to the x axis
shown. At a certain instant, the gear A rotates with WA = 6i rad/s and the gea
rotates with ac = 10i rad/s. Determine 0g and ag of the gear B at this instant
0.6 m
0.9 m
Fig. P15.8
Fig. P15.9*
15.9* A 0.6-m radius drum carrying the load A is rigidly attached to a 0.9-1
pulley carrying the load B as shown. At the time t = 0, the load B moves
velocity of 2 m/s and a constant acceleration of 3 m/s? . Over the time
05152 s, determine (a) the number of revolutions executed by the pulley
displacement of the load A.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F259e4a29-cb7a-42bb-a1a4-7f58c701b1bd%2F21f534a3-4b6e-4b91-953b-d651c0a5272e%2F7ncap62_processed.jpeg&w=3840&q=75)
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