A horizontal spring has a force constant 7.98 N/m and is attached to a wall at one end. A block of wood of mass 366 g is attached to the the other end. We assume that this system sits on a frictionless surface. The block is displaced by +6.90 cm from equilibrium and released from rest. a. What is the period of the motion? S b. What is the equation that describes the position of the block? Make sure to show your work in your notes. O -6.90 ×10*2 m cos (4.67 t) O 6.90 ×10*2 m cos (4.67 t) O 6.90 ×102 m cos (7.98 t+ T/2) 6.90 ×10-2 m cos (7.98 t) -6.90 x10-2 m cos (7.98 t) O 6.90 ×10-2 m cos (4.67 t + TI/2) c. What is the equation that describes the speed of the block? Make sure to show your work in your notes. O -0.322 m/s sin (4.67 t) O -0.551 m/s cos (7.98 t) -0.322 m/s sin (4.67 t + T/2) O -0.551 m/s sin (7.98 t+ 7/2) -0.322 m/s cos (4.67 t) O -0.551 m/s sin (7.98 t)
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.
![A horizontal spring has a force constant 7.98 N/m and is attached to a wall at one end. A block of wood of
mass 366 g is attached to the the other end. We assume that this system sits on a frictionless surface.
The block is displaced by +6.90 cm from equilibrium and released from rest.
a. What is the period of the motion?
S
b. What is the equation that describes the position of the block? Make sure to show your work in your
notes.
-6.90 x102 m cos (4.67 t)
O 6.90 ×102 m cos (4.67 t)
6.90 x102 m cos (7.98 t+ 7/2)
O 6.90 ×102 m cos (7.98 t)
-6.90 x102 m cos (7.98 t)
O 6.90 x102 m cos (4.67 t + T/2)
c. What is the equation that describes the speed of the block? Make sure to show your work in your
notes.
-0.322 m/s sin (4.67 t)
-0.551 m/s cos (7.98 t)
-0.322 m/s sin (4.67 t + T/2)
-0.551 m/s sin (7.98 t+ T/2)
-0.322 m/s cos (4.67 t)
-0.551 m/s sin (7.98 t)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc01f8460-caed-472f-a81b-71765c9566fe%2F8fa5534c-d09f-4372-948b-2afc0317f3c8%2Fuxzna9_processed.png&w=3840&q=75)
![d. The block is now released from the same initial position, but with an initial velocity of -0.144 m/s.
What is the equation that describes the position of the block? Make sure to show your work in your
notes.
-6.90 x102 m cos (7.98 t)
O-7.56 x102 m cos (4.67 t + 0.420 rad)
O7.56 ×102 m cos (4.67 t + 0.420 rad)
7.56 x10-2 m cos (4.67 t - 0.420 rad)
O7.56 x102 m cos (4.67 t)
O 6.90 x102 m cos (4.67 t)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc01f8460-caed-472f-a81b-71765c9566fe%2F8fa5534c-d09f-4372-948b-2afc0317f3c8%2F6k171ft_processed.png&w=3840&q=75)
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