The velocity of the oscillating mass at time
is
or
or
.
Further explanation:
Velocity of a particle or a mass at any instant is defined as the rate of change of position of particle with respect to time.
Mathematically,

If position of a particle or mass is a function of time then velocity of mass at any instant will change with respect to time.
Given:
The position of an oscillating mass varies according to the function
.
Mass of an oscillating object is
.
Concept:
The velocity of mass at any instant is calculated by using the following relation
![\begin{aligned}V(t)&=\frac{{dX\left( t \right)}}{{dt}}\\&=\frac{d}{{dt}}\left[{\left( {2.0{\kern 1pt} {\text{cm}}} \right)\cos \left( {10t} \right)} \right]\\&=-\left( {20\,{\text{cm/s}}}\right)\sin\left( {10t}\right)\\\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7DV%28t%29%26%3D%5Cfrac%7B%7BdX%5Cleft%28%20t%20%5Cright%29%7D%7D%7B%7Bdt%7D%7D%5C%5C%26%3D%5Cfrac%7Bd%7D%7B%7Bdt%7D%7D%5Cleft%5B%7B%5Cleft%28%20%7B2.0%7B%5Ckern%201pt%7D%20%7B%5Ctext%7Bcm%7D%7D%7D%20%5Cright%29%5Ccos%20%5Cleft%28%20%7B10t%7D%20%5Cright%29%7D%20%5Cright%5D%5C%5C%26%3D-%5Cleft%28%20%7B20%5C%2C%7B%5Ctext%7Bcm%2Fs%7D%7D%7D%5Cright%29%5Csin%5Cleft%28%20%7B10t%7D%5Cright%29%5C%5C%5Cend%7Baligned%7D)
Therefore the velocity of the mass at any instant is given by
From the above expression of velocity it can be observed that velocity is changing with time according to the sin function.
Substitute
for t in the above expression

Thus, the velocity of the oscillating mass at time
is
or
or
.
Learn More:
1. The units expressing the rotational velocity brainly.com/question/2887706
2. Find the vertical displacement as a function of time brainly.com/question/2887706
3. A remote controlled car is moving in a vacant parking lot brainly.com/question/2005478
Answer Details:
Grade: College
Subject: Physics
Chapter: Force
Keywords:
position, oscillating, 55 g, mass, time, x(t)=(2.0cm)cos(10t), t=4 s, determine, velocity, 15 cm/s, 0.15 m/s, rate, change in position.