which of the following changes will increase the period of an oscillating spring mass system?
a. an increase in the mass on the spring.
b. an increase in the initial displacement of the spring.
c. an increase in the spring constant.
d. more than one of the above.
e. none of the above.
explain your answer
Is it a. Because increasing mass will increase the period.
To determine which changes will increase the period of an oscillating spring-mass system, let's review the factors that affect the period of such a system.
The period of an oscillating spring-mass system is given by the equation:
T = 2π * √(m/k)
Where T is the period, m is the mass attached to the spring, and k is the spring constant.
Now, let's analyze each option:
a. An increase in the mass on the spring:
According to the equation above, an increase in mass (m) will increase the period (T). This is because the greater the mass, the stronger the inertia, which slows down the oscillation, resulting in a longer period. Therefore, option a is correct.
b. An increase in the initial displacement of the spring:
The initial displacement does not directly affect the period of an oscillating spring-mass system. The period is determined by the mass and the spring constant, not the initial displacement. Therefore, option b is incorrect.
c. An increase in the spring constant:
According to the equation for period, an increase in the spring constant (k) would actually decrease the period (T). This is because a stiffer spring (higher k) will restore the system to equilibrium faster, resulting in a shorter period. Therefore, option c is incorrect.
d. More than one of the above:
As mentioned above, option a is correct, while options b and c are incorrect. Thus, option d is incorrect.
e. None of the above:
Since option a is correct, and none of the other options are entirely correct, option e (none of the above) would be incorrect.
In conclusion, the correct choice is option a. Increasing the mass on the spring will increase the period of an oscillating spring-mass system.
didn't someone already say that the mass has no effect on the period?
Pay atten -- I say -- pay attention, boy!