Complete question:
A 200 g load attached to a horizontal spring moves in simple harmonic motion with a period of 0.410 s. The total mechanical energy of the spring–load system is 2.00 J. Find
(a) the force constant of the spring and (b) the amplitude of the motion.
Answer:
(a) the force constant of the spring = 47 N/m
(b) the amplitude of the motion = 0.292 m
Explanation:
Given;
mass of the spring, m = 200g = 0.2 kg
period of oscillation, T = 0.410 s
total mechanical energy of the spring, E = 2 J
The angular speed is calculated as follows;
(a) the force constant of the spring
(b) the amplitude of the motion
E = ¹/₂kA²
2E = kA²
A² = 2E/k
The statement about pointwise convergence follows because C is a complete metric space. If fn → f uniformly on S, then |fn(z) − fm(z)| ≤ |fn(z) − f(z)| + |f(z) − fm(z)|, hence {fn} is uniformly Cauchy. Conversely, if {fn} is uniformly Cauchy, it is pointwise Cauchy and therefore converges pointwise to a limit function f. If |fn(z)−fm(z)| ≤ ε for all n,m ≥ N and all z ∈ S, let m → ∞ to show that |fn(z)−f(z)|≤εforn≥N andallz∈S. Thusfn →f uniformlyonS.
2. This is immediate from (2.2.7).
3. We have f′(x) = (2/x3)e−1/x2 for x ̸= 0, and f′(0) = limh→0(1/h)e−1/h2 = 0. Since f(n)(x) is of the form pn(1/x)e−1/x2 for x ̸= 0, where pn is a polynomial, an induction argument shows that f(n)(0) = 0 for all n. If g is analytic on D(0,r) and g = f on (−r,r), then by (2.2.16), g(z) =
It’s c, the toy car changes direction
Answer:
18.89cm
Explanation:
As we know that the person is standing 5m in front of the camera
The focal length of the lens =50cm
f=50 cm
By Lens formula we have:
By the formula of magnification
The height of the image formed is 18.89cm.
The fast lap is irrelevant to the question, because it didn't happen
until after the 9 laps that you're interested in.
To be perfectly technical about it, we don't actually have enough
information to answer the question. You told us her average speed
for 10 laps, but we don't know anything about how her speed may
have changed during the whole 10 laps. For all we know, maybe
she took a nap first, and then got up and drove 10 laps at the speed
of 125 metres per second. That would produce the average speed
of 12.5 metres per second and we would never know it Why not ?
That's only 280 miles per hour. Bikes can do that, can't they ?
IF we can assume that Amy maintained a totally steady pace through
the entire 10 laps, then we could say that her average for 9 laps was
also 12.5 metres per second.
